Background

This analysis document compliments FIA NLS Models: Biomass Growth vs. Biomass. All of the background information from that document applies to these analyses, which are extensions to them. The difference between that document and this analysis is the use of different growth estimators.

Here, we fit the models using: 1) calculated plot biomass growth (Mass-Balance method) using only trees >5 inches (12.5 cm) dbh (\(G_{MassBal > 5}\)), and 2) plot biomass growth (tree incremental growth method \(G_{TI}\) for trees >5 inches (12.5 cm) dbh (\(G_{TI-NoIngrow}\)).

Below the model fitting procedure is implemented by ecoprovince:

Analysis 1: \(G_{MassBal > 5}\)

211 - Northeastern Mixed Forest

Model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   6822     6268.0                                
## 2   6821     6253.9  1 14.031  15.303 9.244e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 26129.23
## 2     2 26115.94
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * 
##     (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau     1.0226     0.2280   4.485 7.41e-06 ***
## alpha   0.1515     0.0381   3.975 7.10e-05 ***
## A       3.5870     0.1490  24.072  < 2e-16 ***
## k      32.1364     1.7469  18.396  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9575 on 6821 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 5.408e-07
##   (52 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

Model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "a", "_MBg5", sep = "")), data = G_211,  : 
##   parameters without starting value in 'data': tau
## Error in nls(get(paste("fg_", Mod.Sel1, "b", "_MBg5", sep = "")), data = G_211,  : 
##   parameters without starting value in 'data': tau
## Error in nls(get(paste("fg_", Mod.Sel1, "c", "_MBg5", sep = "")), data = G_211,  : 
##   parameters without starting value in 'data': tau
##   model      AIC
## 1     2 26115.94
## 2    2a       NA
## 3    2b       NA
## 4    2c       NA
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * 
##     (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau     1.0226     0.2280   4.485 7.41e-06 ***
## alpha   0.1515     0.0381   3.975 7.10e-05 ***
## A       3.5870     0.1490  24.072  < 2e-16 ***
## k      32.1364     1.7469  18.396  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9575 on 6821 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 5.408e-07
##   (52 observations deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

predict and plot

## Warning: Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
## ℹ Please use `linewidth` instead.
## Warning: Removed 17 rows containing missing values (`geom_point()`).
## Warning: Removed 1038 rows containing missing values (`geom_line()`).

plotting 2

212 - Laurentian Mixed Forest

Model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1  18911      19584                                
## 2  18910      19475  1 109.64  106.46 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 67445.37
## 2     2 67341.19
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * 
##     (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    1.33873    0.18303   7.314 2.69e-13 ***
## alpha  0.27311    0.02566  10.643  < 2e-16 ***
## A      3.21539    0.09883  32.535  < 2e-16 ***
## k     43.84726    1.49165  29.395  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.015 on 18910 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 1.353e-06
##   (3801 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

Model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "a", "_MBg5", sep = "")), data = G_212,  : 
##   parameters without starting value in 'data': tau
## Error in nls(get(paste("fg_", Mod.Sel1, "b", "_MBg5", sep = "")), data = G_212,  : 
##   parameters without starting value in 'data': tau
## Error in nls(get(paste("fg_", Mod.Sel1, "c", "_MBg5", sep = "")), data = G_212,  : 
##   parameters without starting value in 'data': tau
##   model      AIC
## 1     2 67341.19
## 2    2a       NA
## 3    2b       NA
## 4    2c       NA
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * 
##     (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    1.33873    0.18303   7.314 2.69e-13 ***
## alpha  0.27311    0.02566  10.643  < 2e-16 ***
## A      3.21539    0.09883  32.535  < 2e-16 ***
## k     43.84726    1.49165  29.395  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.015 on 18910 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 1.353e-06
##   (3801 observations deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

predict and plot

## Warning: Removed 1926 rows containing missing values (`geom_point()`).
## Warning: Removed 1031 rows containing missing values (`geom_line()`).

plotting 2

221 - Eastern Broadleaf Forest

Model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   7266     9818.9                                
## 2   7265     9612.0  1 206.84  156.33 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 32046.10
## 2     2 31893.34
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * 
##     (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau   -0.86021    0.11923  -7.215 5.94e-13 ***
## alpha  0.52324    0.03993  13.102  < 2e-16 ***
## A      5.93232    0.20274  29.261  < 2e-16 ***
## k     32.54201    2.57514  12.637  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.15 on 7265 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 2.662e-06
##   (64 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

Model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "a", "_MBg5", sep = "")), data = G_221,  : 
##   parameters without starting value in 'data': tau
## Error in nls(get(paste("fg_", Mod.Sel1, "b", "_MBg5", sep = "")), data = G_221,  : 
##   parameters without starting value in 'data': tau
## Error in nls(get(paste("fg_", Mod.Sel1, "c", "_MBg5", sep = "")), data = G_221,  : 
##   parameters without starting value in 'data': tau
##   model      AIC
## 1     2 31893.34
## 2    2a       NA
## 3    2b       NA
## 4    2c       NA
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * 
##     (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau   -0.86021    0.11923  -7.215 5.94e-13 ***
## alpha  0.52324    0.03993  13.102  < 2e-16 ***
## A      5.93232    0.20274  29.261  < 2e-16 ***
## k     32.54201    2.57514  12.637  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.15 on 7265 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 2.662e-06
##   (64 observations deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

predict and plot

## Warning: Removed 32 rows containing missing values (`geom_point()`).
## Warning: Removed 1036 rows containing missing values (`geom_line()`).

plotting 2

222 - Midwest Broadleaf Forest

Model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   4839     5394.3                                
## 2   4838     5314.0  1 80.317  73.123 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 19469.00
## 2     2 19398.36
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * 
##     (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    0.06034    0.21585   0.280     0.78    
## alpha  0.42894    0.04778   8.978   <2e-16 ***
## A      5.05639    0.23881  21.174   <2e-16 ***
## k     41.09173    2.77384  14.814   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.048 on 4838 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 5.802e-06
##   (1003 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

Model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "a", "_MBg5", sep = "")), data = G_222,  : 
##   parameters without starting value in 'data': tau
## Error in nls(get(paste("fg_", Mod.Sel1, "b", "_MBg5", sep = "")), data = G_222,  : 
##   parameters without starting value in 'data': tau
## Error in nls(get(paste("fg_", Mod.Sel1, "c", "_MBg5", sep = "")), data = G_222,  : 
##   parameters without starting value in 'data': tau
##   model      AIC
## 1     2 19398.36
## 2    2a       NA
## 3    2b       NA
## 4    2c       NA
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * 
##     (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    0.06034    0.21585   0.280     0.78    
## alpha  0.42894    0.04778   8.978   <2e-16 ***
## A      5.05639    0.23881  21.174   <2e-16 ***
## k     41.09173    2.77384  14.814   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.048 on 4838 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 5.802e-06
##   (1003 observations deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

predict and plot

## Warning: Removed 489 rows containing missing values (`geom_point()`).
## Warning: Removed 1053 rows containing missing values (`geom_line()`).

plotting 2

223 - Central Interior Broadleaf Forest

Model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   8742      10361                                
## 2   8741      10217  1 143.46  122.73 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 35815.03
## 2     2 35695.10
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * 
##     (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau   -0.81212    0.10812  -7.511 6.43e-14 ***
## alpha  0.47384    0.04076  11.626  < 2e-16 ***
## A      6.29354    0.22631  27.809  < 2e-16 ***
## k     62.38730    4.20500  14.836  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.081 on 8741 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 6.781e-06
##   (1265 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

Model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "a", "_MBg5", sep = "")), data = G_223,  : 
##   parameters without starting value in 'data': tau
## Error in nls(get(paste("fg_", Mod.Sel1, "b", "_MBg5", sep = "")), data = G_223,  : 
##   parameters without starting value in 'data': tau
## Error in nls(get(paste("fg_", Mod.Sel1, "c", "_MBg5", sep = "")), data = G_223,  : 
##   parameters without starting value in 'data': tau
##   model     AIC
## 1     2 35695.1
## 2    2a      NA
## 3    2b      NA
## 4    2c      NA
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * 
##     (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau   -0.81212    0.10812  -7.511 6.43e-14 ***
## alpha  0.47384    0.04076  11.626  < 2e-16 ***
## A      6.29354    0.22631  27.809  < 2e-16 ***
## k     62.38730    4.20500  14.836  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.081 on 8741 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 6.781e-06
##   (1265 observations deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

predict and plot

## Warning: Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
## ℹ Please use `linewidth` instead.
## Warning: Removed 620 rows containing missing values (`geom_point()`).
## Warning: Removed 1002 rows containing missing values (`geom_line()`).

plotting 2

231 - Southeastern Mixed Forest

Model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1  13233      28484                                
## 2  13232      27214  1 1269.8   617.4 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 66709.26
## 2     2 66107.65
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * 
##     (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    2.05100    0.21819    9.40   <2e-16 ***
## alpha  0.57826    0.02162   26.75   <2e-16 ***
## A      4.03929    0.13015   31.04   <2e-16 ***
## k     12.85831    0.73266   17.55   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.434 on 13232 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 2.169e-06
##   (281 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

Model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "a", "_MBg5", sep = "")), data = G_231,  : 
##   parameters without starting value in 'data': tau
## Error in nls(get(paste("fg_", Mod.Sel1, "b", "_MBg5", sep = "")), data = G_231,  : 
##   parameters without starting value in 'data': tau
## Error in nls(get(paste("fg_", Mod.Sel1, "c", "_MBg5", sep = "")), data = G_231,  : 
##   parameters without starting value in 'data': tau
##   model      AIC
## 1     2 66107.65
## 2    2a       NA
## 3    2b       NA
## 4    2c       NA
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * 
##     (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    2.05100    0.21819    9.40   <2e-16 ***
## alpha  0.57826    0.02162   26.75   <2e-16 ***
## A      4.03929    0.13015   31.04   <2e-16 ***
## k     12.85831    0.73266   17.55   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.434 on 13232 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 2.169e-06
##   (281 observations deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

predict and plot

## Warning: Removed 143 rows containing missing values (`geom_point()`).
## Warning: Removed 1017 rows containing missing values (`geom_line()`).

plotting 2

232 - Outer Coastal Plain Mixed Forest

Model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1  13303      32383                                
## 2  13302      31089  1 1294.5   553.9 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 67119.92
## 2     2 66579.08
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * 
##     (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    1.28290    0.19506   6.577 4.98e-11 ***
## alpha  0.55302    0.02165  25.546  < 2e-16 ***
## A      4.56589    0.15267  29.906  < 2e-16 ***
## k     19.58218    0.99760  19.629  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.529 on 13302 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 1.537e-06
##   (323 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

Model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "a", "_MBg5", sep = "")), data = G_232,  : 
##   parameters without starting value in 'data': tau
## Error in nls(get(paste("fg_", Mod.Sel1, "b", "_MBg5", sep = "")), data = G_232,  : 
##   parameters without starting value in 'data': tau
## Error in nls(get(paste("fg_", Mod.Sel1, "c", "_MBg5", sep = "")), data = G_232,  : 
##   parameters without starting value in 'data': tau
##   model      AIC
## 1     2 66579.08
## 2    2a       NA
## 3    2b       NA
## 4    2c       NA
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * 
##     (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    1.28290    0.19506   6.577 4.98e-11 ***
## alpha  0.55302    0.02165  25.546  < 2e-16 ***
## A      4.56589    0.15267  29.906  < 2e-16 ***
## k     19.58218    0.99760  19.629  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.529 on 13302 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 1.537e-06
##   (323 observations deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

predict and plot

## Warning: Removed 169 rows containing missing values (`geom_point()`).
## Warning: Removed 931 rows containing missing values (`geom_line()`).

plotting 2

234 - Lower Mississippi Riverine Forest

Model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   1324     3585.5                                
## 2   1323     3430.0  1 155.55  59.998 1.879e-14 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 6935.007
## 2     2 6878.152
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * 
##     (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    1.38770    0.89916   1.543    0.123    
## alpha  0.72003    0.08454   8.517  < 2e-16 ***
## A      4.09026    0.61709   6.628 4.93e-11 ***
## k     12.26760    2.92583   4.193 2.94e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.61 on 1323 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 3.486e-06
##   (61 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

Model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "a", "_MBg5", sep = "")), data = G_234,  : 
##   parameters without starting value in 'data': tau
## Error in nls(get(paste("fg_", Mod.Sel1, "b", "_MBg5", sep = "")), data = G_234,  : 
##   parameters without starting value in 'data': tau
## Error in nls(get(paste("fg_", Mod.Sel1, "c", "_MBg5", sep = "")), data = G_234,  : 
##   parameters without starting value in 'data': tau
##   model      AIC
## 1     2 6878.152
## 2    2a       NA
## 3    2b       NA
## 4    2c       NA
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * 
##     (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    1.38770    0.89916   1.543    0.123    
## alpha  0.72003    0.08454   8.517  < 2e-16 ***
## A      4.09026    0.61709   6.628 4.93e-11 ***
## k     12.26760    2.92583   4.193 2.94e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.61 on 1323 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 3.486e-06
##   (61 observations deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.91191, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -4.5683, p-value = 4.916e-06
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 27 rows containing missing values (`geom_point()`).
## Warning: Removed 645 rows containing missing values (`geom_line()`).

plotting 2

242 - Pacific Lowland Mixed Forest

Model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value  Pr(>F)  
## 1     77     134.46                            
## 2     76     125.84  1 8.6128  5.2016 0.02537 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 422.9552
## 2     2 419.6591
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * 
##     (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)  
## tau    -0.1712     2.5098  -0.068   0.9458  
## alpha   0.8913     0.3544   2.515   0.0140 *
## A       8.5388     4.6759   1.826   0.0718 .
## k      29.0699    15.4743   1.879   0.0641 .
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.287 on 76 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 3.566e-06
##   (3 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

Model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "a", "_MBg5", sep = "")), data = G_242,  : 
##   parameters without starting value in 'data': tau
## Error in nls(get(paste("fg_", Mod.Sel1, "b", "_MBg5", sep = "")), data = G_242,  : 
##   parameters without starting value in 'data': tau
## Error in nls(get(paste("fg_", Mod.Sel1, "c", "_MBg5", sep = "")), data = G_242,  : 
##   parameters without starting value in 'data': tau
##   model      AIC
## 1     2 419.6591
## 2    2a       NA
## 3    2b       NA
## 4    2c       NA
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * 
##     (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)  
## tau    -0.1712     2.5098  -0.068   0.9458  
## alpha   0.8913     0.3544   2.515   0.0140 *
## A       8.5388     4.6759   1.826   0.0718 .
## k      29.0699    15.4743   1.879   0.0641 .
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.287 on 76 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 3.566e-06
##   (3 observations deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.90404, p-value = 1.812e-05
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = 0.28449, p-value = 0.776
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 2 rows containing missing values (`geom_point()`).
## Warning: Removed 725 rows containing missing values (`geom_line()`).

plotting 2

251 - Prairie Parkland (Temperate)

Model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1   1785     2660.0                         
## 2   1784     2658.8  1 1.1725  0.7867 0.3752
##   model      AIC
## 1     1 7632.934
## 2     2 7634.145
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * 
##     A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##     Estimate Std. Error t value Pr(>|t|)    
## tau   0.4527     0.4946   0.915     0.36    
## A     3.4709     0.3419  10.151  < 2e-16 ***
## k    24.0566     4.2655   5.640 1.98e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.221 on 1785 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 4.972e-06
##   (507 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

Model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "a", "_MBg5", sep = "")), data = G_251,  : 
##   parameters without starting value in 'data': tau
## Error in nls(get(paste("fg_", Mod.Sel1, "b", "_MBg5", sep = "")), data = G_251,  : 
##   parameters without starting value in 'data': tau
## Error in nls(get(paste("fg_", Mod.Sel1, "c", "_MBg5", sep = "")), data = G_251,  : 
##   parameters without starting value in 'data': tau
##   model      AIC
## 1     1 7632.934
## 2    1a       NA
## 3    1b       NA
## 4    1c       NA
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * 
##     A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##     Estimate Std. Error t value Pr(>|t|)    
## tau   0.4527     0.4946   0.915     0.36    
## A     3.4709     0.3419  10.151  < 2e-16 ***
## k    24.0566     4.2655   5.640 1.98e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.221 on 1785 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 4.972e-06
##   (507 observations deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.69868, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -7.6629, p-value = 1.818e-14
## alternative hypothesis: two.sided

predict and plot

## Warning: Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
## ℹ Please use `linewidth` instead.
## Warning: Removed 254 rows containing missing values (`geom_point()`).
## Warning: Removed 1176 rows containing missing values (`geom_line()`).

plotting 2

255 - Prairie Parkland (Subtropical)

Model selection 1

## Error in nls(fg_1_MBg5, data = G_255, start = c(tau = tau.start, A = A.start,  : 
##   number of iterations exceeded maximum of 50
## Error in nls(fg_2_MBg5, data = G_255, start = c(tau = tau.start, alpha = alpha.start,  : 
##   number of iterations exceeded maximum of 50
##   model AIC
## 1     1  NA
## 2     2  NA
## Warning in min(AIC1_255$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in h(simpleError(msg, call)) : 
##   error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_255.' not found

summary

  • simple model: does not fit
  • alpha model: does not fit

Model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

261 - California Coastal Chaparral Forest and Shrub

Model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

Model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

262 - California Dry Steppe

Model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

Model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

263 - California Coastal Steppe - Mixed Forest and Redwood Forest

Model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

Model selection 2

summary

  • add p model: does not fit

  • add s model: does not fit

  • add s+p model: does not fit

  • note: model fit, but fit was funky due to data being sparse

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

313 - Colorado Plateau Semi-Desert

Model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value   Pr(>F)   
## 1    212     98.175                              
## 2    211     95.055  1   3.12  6.9257 0.009124 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 485.5008
## 2     2 480.5572
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * 
##     (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)   
## tau    -1.2288     0.8965  -1.371  0.17194   
## alpha   0.7287     0.2474   2.946  0.00358 **
## A       4.5680     1.4482   3.154  0.00184 **
## k     120.2565    37.7272   3.188  0.00165 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6712 on 211 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 1.419e-06
##   (3 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

Model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "a", "_MBg5", sep = "")), data = G_313,  : 
##   parameters without starting value in 'data': tau
## Error in nls(get(paste("fg_", Mod.Sel1, "b", "_MBg5", sep = "")), data = G_313,  : 
##   parameters without starting value in 'data': tau
## Error in nls(get(paste("fg_", Mod.Sel1, "c", "_MBg5", sep = "")), data = G_313,  : 
##   parameters without starting value in 'data': tau
##   model      AIC
## 1     2 480.5572
## 2    2a       NA
## 3    2b       NA
## 4    2c       NA
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * 
##     (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)   
## tau    -1.2288     0.8965  -1.371  0.17194   
## alpha   0.7287     0.2474   2.946  0.00358 **
## A       4.5680     1.4482   3.154  0.00184 **
## k     120.2565    37.7272   3.188  0.00165 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6712 on 211 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 1.419e-06
##   (3 observations deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.97747, p-value = 0.001613
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -0.06549, p-value = 0.9478
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 1103 rows containing missing values (`geom_line()`).

plotting 2

315 - Southwest Plateau and Plains Dry Steppe and Shrub

Model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

Model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

321 - Chihuahuan Semi-Desert

Model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

Model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

322 - American Semidesert and Desert

Model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

Model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

331 - Great Plains/Palouse Dry Steppe

Model selection 1

## Error in nls(fg_1_MBg5, data = G_331, start = c(tau = tau.start, A = A.start,  : 
##   number of iterations exceeded maximum of 50
## Error in nls(fg_2_MBg5, data = G_331, start = c(tau = tau.start, alpha = alpha.start,  : 
##   number of iterations exceeded maximum of 50
##   model AIC
## 1     1  NA
## 2     2  NA
## Warning in min(AIC1_331$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in h(simpleError(msg, call)) : 
##   error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_331.' not found

summary

  • simple model: does not fit
  • alpha model: does not fit

Model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

332 - Great Plains Steppe

Model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1    193     155.63                          
## 2    192     155.46  1 0.16853  0.2081 0.6487
##   model      AIC
## 1     1 637.9079
## 2     2 639.6956
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * 
##     A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##     Estimate Std. Error t value Pr(>|t|)   
## tau   0.3291     1.3677   0.241  0.81011   
## A     4.3422     1.3161   3.299  0.00115 **
## k    74.7556    23.5156   3.179  0.00172 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.898 on 193 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 2.347e-06
##   (36 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

Model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "a", "_MBg5", sep = "")), data = G_332,  : 
##   parameters without starting value in 'data': tau
## Error in nls(get(paste("fg_", Mod.Sel1, "b", "_MBg5", sep = "")), data = G_332,  : 
##   parameters without starting value in 'data': tau
## Error in nls(get(paste("fg_", Mod.Sel1, "c", "_MBg5", sep = "")), data = G_332,  : 
##   parameters without starting value in 'data': tau
##   model      AIC
## 1     1 637.9079
## 2    1a       NA
## 3    1b       NA
## 4    1c       NA
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * 
##     A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##     Estimate Std. Error t value Pr(>|t|)   
## tau   0.3291     1.3677   0.241  0.81011   
## A     4.3422     1.3161   3.299  0.00115 **
## k    74.7556    23.5156   3.179  0.00172 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.898 on 193 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 2.347e-06
##   (36 observations deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.89621, p-value = 1.963e-10
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -1.2715, p-value = 0.2035
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 18 rows containing missing values (`geom_point()`).
## Warning: Removed 1120 rows containing missing values (`geom_line()`).

plotting 2

341 - Intermountain Semi-desert & Desert

Model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

Model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

342 - Intermountain Semi-Desert

Model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value   Pr(>F)   
## 1    112     71.868                              
## 2    111     65.507  1 6.3609  10.778 0.001374 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 293.4221
## 2     2 284.7648
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * 
##     (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau      2.873      6.589   0.436 0.663615    
## alpha    0.888      0.235   3.779 0.000255 ***
## A        2.919      2.546   1.146 0.254058    
## k       90.854     34.235   2.654 0.009126 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7682 on 111 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 7.021e-06
##   (9 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

Model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "a", "_MBg5", sep = "")), data = G_342,  : 
##   parameters without starting value in 'data': tau
## Error in nls(get(paste("fg_", Mod.Sel1, "b", "_MBg5", sep = "")), data = G_342,  : 
##   parameters without starting value in 'data': tau
## Error in nls(get(paste("fg_", Mod.Sel1, "c", "_MBg5", sep = "")), data = G_342,  : 
##   parameters without starting value in 'data': tau
##   model      AIC
## 1     2 284.7648
## 2    2a       NA
## 3    2b       NA
## 4    2c       NA
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * 
##     (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau      2.873      6.589   0.436 0.663615    
## alpha    0.888      0.235   3.779 0.000255 ***
## A        2.919      2.546   1.146 0.254058    
## k       90.854     34.235   2.654 0.009126 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7682 on 111 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 7.021e-06
##   (9 observations deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.94429, p-value = 0.0001199
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -0.94042, p-value = 0.347
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 4 rows containing missing values (`geom_point()`).
## Warning: Removed 1241 rows containing missing values (`geom_line()`).

plotting 2

411 - Everglades

Model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

Model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M211 - Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow

Model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   6746     5130.8                                
## 2   6745     5102.6  1 28.237  37.326 1.055e-09 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 24245.14
## 2     2 24209.89
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * 
##     (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    1.77864    0.28950   6.144 8.51e-10 ***
## alpha  0.20350    0.03252   6.257 4.15e-10 ***
## A      2.99829    0.14210  21.101  < 2e-16 ***
## k     33.06165    1.76977  18.681  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8698 on 6745 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 6.312e-06
##   (23 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

Model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "a", "_MBg5", sep = "")), data = G_M211,  : 
##   parameters without starting value in 'data': tau
## Error in nls(get(paste("fg_", Mod.Sel1, "b", "_MBg5", sep = "")), data = G_M211,  : 
##   parameters without starting value in 'data': tau
## Error in nls(get(paste("fg_", Mod.Sel1, "c", "_MBg5", sep = "")), data = G_M211,  : 
##   parameters without starting value in 'data': tau
##   model      AIC
## 1     2 24209.89
## 2    2a       NA
## 3    2b       NA
## 4    2c       NA
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * 
##     (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    1.77864    0.28950   6.144 8.51e-10 ***
## alpha  0.20350    0.03252   6.257 4.15e-10 ***
## A      2.99829    0.14210  21.101  < 2e-16 ***
## k     33.06165    1.76977  18.681  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8698 on 6745 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 6.312e-06
##   (23 observations deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

predict and plot

## Warning: Removed 14 rows containing missing values (`geom_point()`).
## Warning: Removed 1108 rows containing missing values (`geom_line()`).

plotting 2

M221 - Eastern Broadleaf Forest

Model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   8257      15147                                
## 2   8256      14972  1 174.97  96.483 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 39278.06
## 2     2 39184.09
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * 
##     (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    0.01062    0.15916   0.067    0.947    
## alpha  0.56783    0.05558  10.217   <2e-16 ***
## A      4.80611    0.18242  26.347   <2e-16 ***
## k     27.74238    2.78273   9.969   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.347 on 8256 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 8.228e-06
##   (55 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

Model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "a", "_MBg5", sep = "")), data = G_M221,  : 
##   parameters without starting value in 'data': tau
## Error in nls(get(paste("fg_", Mod.Sel1, "b", "_MBg5", sep = "")), data = G_M221,  : 
##   parameters without starting value in 'data': tau
## Error in nls(get(paste("fg_", Mod.Sel1, "c", "_MBg5", sep = "")), data = G_M221,  : 
##   parameters without starting value in 'data': tau
##   model      AIC
## 1     2 39184.09
## 2    2a       NA
## 3    2b       NA
## 4    2c       NA
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * 
##     (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    0.01062    0.15916   0.067    0.947    
## alpha  0.56783    0.05558  10.217   <2e-16 ***
## A      4.80611    0.18242  26.347   <2e-16 ***
## k     27.74238    2.78273   9.969   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.347 on 8256 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 8.228e-06
##   (55 observations deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

predict and plot

## Warning: Removed 27 rows containing missing values (`geom_point()`).
## Warning: Removed 982 rows containing missing values (`geom_line()`).

plotting 2

M223 - Ozark Broadleaf Forest Meadow

Model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value   Pr(>F)   
## 1    887     1241.7                              
## 2    886     1231.0  1 10.651  7.6657 0.005745 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 3673.208
## 2     2 3667.540
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * 
##     (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau     2.3199     1.2375   1.875  0.06117 .  
## alpha   0.4618     0.1599   2.889  0.00396 ** 
## A       2.4511     0.4773   5.136 3.46e-07 ***
## k      31.9347    10.1809   3.137  0.00176 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.179 on 886 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 7.832e-06
##   (6 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

Model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "a", "_MBg5", sep = "")), data = G_M223,  : 
##   parameters without starting value in 'data': tau
## Error in nls(get(paste("fg_", Mod.Sel1, "b", "_MBg5", sep = "")), data = G_M223,  : 
##   parameters without starting value in 'data': tau
## Error in nls(get(paste("fg_", Mod.Sel1, "c", "_MBg5", sep = "")), data = G_M223,  : 
##   parameters without starting value in 'data': tau
##   model     AIC
## 1     2 3667.54
## 2    2a      NA
## 3    2b      NA
## 4    2c      NA
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * 
##     (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau     2.3199     1.2375   1.875  0.06117 .  
## alpha   0.4618     0.1599   2.889  0.00396 ** 
## A       2.4511     0.4773   5.136 3.46e-07 ***
## k      31.9347    10.1809   3.137  0.00176 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.179 on 886 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 7.832e-06
##   (6 observations deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.93319, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -2.1934, p-value = 0.02828
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 6 rows containing missing values (`geom_point()`).
## Warning: Removed 1175 rows containing missing values (`geom_line()`).

plotting 2

M231 - Ouachita Mixed Forest

Model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1    989     1325.2                                
## 2    988     1309.2  1 16.095  12.147 0.0005134 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 4081.795
## 2     2 4071.673
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * 
##     (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau     3.6087     1.7664   2.043 0.041328 *  
## alpha   0.3982     0.1098   3.625 0.000303 ***
## A       2.3591     0.5308   4.445 9.81e-06 ***
## k      34.1285     7.1289   4.787 1.95e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.151 on 988 degrees of freedom
## 
## Number of iterations to convergence: 11 
## Achieved convergence tolerance: 4.638e-06
##   (14 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

Model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "a", "_MBg5", sep = "")), data = G_M231,  : 
##   parameters without starting value in 'data': tau
## Error in nls(get(paste("fg_", Mod.Sel1, "b", "_MBg5", sep = "")), data = G_M231,  : 
##   parameters without starting value in 'data': tau
## Error in nls(get(paste("fg_", Mod.Sel1, "c", "_MBg5", sep = "")), data = G_M231,  : 
##   parameters without starting value in 'data': tau
##   model      AIC
## 1     2 4071.673
## 2    2a       NA
## 3    2b       NA
## 4    2c       NA
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * 
##     (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau     3.6087     1.7664   2.043 0.041328 *  
## alpha   0.3982     0.1098   3.625 0.000303 ***
## A       2.3591     0.5308   4.445 9.81e-06 ***
## k      34.1285     7.1289   4.787 1.95e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.151 on 988 degrees of freedom
## 
## Number of iterations to convergence: 11 
## Achieved convergence tolerance: 4.638e-06
##   (14 observations deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.93428, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -4.4777, p-value = 7.547e-06
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 7 rows containing missing values (`geom_point()`).
## Warning: Removed 1218 rows containing missing values (`geom_line()`).

plotting 2

M242 - Cascade Mixed Forest

Model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   3147     8391.5                                
## 2   3146     8049.3  1 342.15  133.72 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 16065.44
## 2     2 15936.31
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * 
##     (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau    -1.69672    0.23864   -7.11 1.43e-12 ***
## alpha   0.90419    0.07101   12.73  < 2e-16 ***
## A      13.03876    1.08531   12.01  < 2e-16 ***
## k     140.11490   11.12055   12.60  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.6 on 3146 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 7.442e-06
##   (74 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

Model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "a", "_MBg5", sep = "")), data = G_M242,  : 
##   parameters without starting value in 'data': tau
## Error in nls(get(paste("fg_", Mod.Sel1, "b", "_MBg5", sep = "")), data = G_M242,  : 
##   parameters without starting value in 'data': tau
## Error in nls(get(paste("fg_", Mod.Sel1, "c", "_MBg5", sep = "")), data = G_M242,  : 
##   parameters without starting value in 'data': tau
##   model      AIC
## 1     2 15936.31
## 2    2a       NA
## 3    2b       NA
## 4    2c       NA
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * 
##     (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau    -1.69672    0.23864   -7.11 1.43e-12 ***
## alpha   0.90419    0.07101   12.73  < 2e-16 ***
## A      13.03876    1.08531   12.01  < 2e-16 ***
## k     140.11490   11.12055   12.60  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.6 on 3146 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 7.442e-06
##   (74 observations deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.9273, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -4.7199, p-value = 2.36e-06
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 39 rows containing missing values (`geom_point()`).
## Warning: Removed 126 rows containing missing values (`geom_line()`).

plotting 2

M261 - Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow

Model selection 1

## Error in as.formula(formula) : object 'fg_3_MBg5' not found
## Analysis of Variance Table
## 
## Model 1: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   1682     3596.1                                
## 2   1681     3529.9  1 66.205  31.528 2.296e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 7923.648
## 2     2 7894.338
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * 
##     (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    -1.5662     0.3694  -4.240 2.35e-05 ***
## alpha   0.6405     0.1065   6.017 2.18e-09 ***
## A      15.1529     1.8631   8.133 8.04e-16 ***
## k     247.1243    29.7556   8.305  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.449 on 1681 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 6.227e-06
##   (292 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

Model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "a", "_MBg5", sep = "")), data = G_M261,  : 
##   parameters without starting value in 'data': tau
## Error in nls(get(paste("fg_", Mod.Sel1, "b", "_MBg5", sep = "")), data = G_M261,  : 
##   parameters without starting value in 'data': tau
## Error in nls(get(paste("fg_", Mod.Sel1, "c", "_MBg5", sep = "")), data = G_M261,  : 
##   parameters without starting value in 'data': tau
##   model      AIC
## 1     2 7894.338
## 2    2a       NA
## 3    2b       NA
## 4    2c       NA
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * 
##     (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    -1.5662     0.3694  -4.240 2.35e-05 ***
## alpha   0.6405     0.1065   6.017 2.18e-09 ***
## A      15.1529     1.8631   8.133 8.04e-16 ***
## k     247.1243    29.7556   8.305  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.449 on 1681 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 6.227e-06
##   (292 observations deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.89716, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -2.1811, p-value = 0.02917
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 155 rows containing missing values (`geom_point()`).

plotting 2

M262 - Califormia Coastal Range = Coniferous Forest - Open woodland Shrub Meadow

Model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

Model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M313 - Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow

Model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1    363     164.19                                
## 2    362     155.26  1 8.9317  20.825 6.902e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 863.6187
## 2     2 845.1470
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * 
##     (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    -2.1151     0.3241  -6.526 2.28e-10 ***
## alpha   0.5769     0.1140   5.061 6.64e-07 ***
## A       9.0519     1.6558   5.467 8.55e-08 ***
## k     153.8173    35.7964   4.297 2.23e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6549 on 362 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 3.706e-06
##   (1 observation deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

Model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "a", "_MBg5", sep = "")), data = G_M313,  : 
##   parameters without starting value in 'data': tau
## Error in nls(get(paste("fg_", Mod.Sel1, "b", "_MBg5", sep = "")), data = G_M313,  : 
##   parameters without starting value in 'data': tau
## Error in nls(get(paste("fg_", Mod.Sel1, "c", "_MBg5", sep = "")), data = G_M313,  : 
##   parameters without starting value in 'data': tau
##   model     AIC
## 1     2 845.147
## 2    2a      NA
## 3    2b      NA
## 4    2c      NA
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * 
##     (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    -2.1151     0.3241  -6.526 2.28e-10 ***
## alpha   0.5769     0.1140   5.061 6.64e-07 ***
## A       9.0519     1.6558   5.467 8.55e-08 ***
## k     153.8173    35.7964   4.297 2.23e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6549 on 362 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 3.706e-06
##   (1 observation deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.96978, p-value = 6.75e-07
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = 0.20111, p-value = 0.8406
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 1183 rows containing missing values (`geom_line()`).

plotting 2

M331 - Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow

Model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   1732     1437.1                                
## 2   1731     1365.6  1 71.524  90.662 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 4817.306
## 2     2 4730.734
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * 
##     (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau   -0.70648    0.56744  -1.245    0.213    
## alpha  0.61261    0.05552  11.034  < 2e-16 ***
## A      2.71538    0.41186   6.593 5.71e-11 ***
## k     49.20052    7.28457   6.754 1.96e-11 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8882 on 1731 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 5.632e-06
##   (21 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

Model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "a", "_MBg5", sep = "")), data = G_M331,  : 
##   parameters without starting value in 'data': tau
## Error in nls(get(paste("fg_", Mod.Sel1, "b", "_MBg5", sep = "")), data = G_M331,  : 
##   parameters without starting value in 'data': tau
## Error in nls(get(paste("fg_", Mod.Sel1, "c", "_MBg5", sep = "")), data = G_M331,  : 
##   parameters without starting value in 'data': tau
##   model      AIC
## 1     2 4730.734
## 2    2a       NA
## 3    2b       NA
## 4    2c       NA
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * 
##     (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau   -0.70648    0.56744  -1.245    0.213    
## alpha  0.61261    0.05552  11.034  < 2e-16 ***
## A      2.71538    0.41186   6.593 5.71e-11 ***
## k     49.20052    7.28457   6.754 1.96e-11 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8882 on 1731 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 5.632e-06
##   (21 observations deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.84462, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -5.8623, p-value = 4.565e-09
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 7 rows containing missing values (`geom_point()`).
## Warning: Removed 1091 rows containing missing values (`geom_line()`).

plotting 2

M332 - Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow

Model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   2513     2563.7                                
## 2   2512     2382.2  1 181.47  191.35 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 8302.884
## 2     2 8120.177
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * 
##     (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau   -0.85974    0.41763  -2.059   0.0396 *  
## alpha  0.77968    0.04943  15.773  < 2e-16 ***
## A      5.26625    0.64151   8.209 3.52e-16 ***
## k     87.68462    9.15787   9.575  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9738 on 2512 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 8.659e-06
##   (96 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

Model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "a", "_MBg5", sep = "")), data = G_M332,  : 
##   parameters without starting value in 'data': tau
## Error in nls(get(paste("fg_", Mod.Sel1, "b", "_MBg5", sep = "")), data = G_M332,  : 
##   parameters without starting value in 'data': tau
## Error in nls(get(paste("fg_", Mod.Sel1, "c", "_MBg5", sep = "")), data = G_M332,  : 
##   parameters without starting value in 'data': tau
##   model      AIC
## 1     2 8120.177
## 2    2a       NA
## 3    2b       NA
## 4    2c       NA
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * 
##     (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau   -0.85974    0.41763  -2.059   0.0396 *  
## alpha  0.77968    0.04943  15.773  < 2e-16 ***
## A      5.26625    0.64151   8.209 3.52e-16 ***
## k     87.68462    9.15787   9.575  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9738 on 2512 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 8.659e-06
##   (96 observations deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.90151, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -6.5103, p-value = 7.503e-11
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 46 rows containing missing values (`geom_point()`).
## Warning: Removed 1001 rows containing missing values (`geom_line()`).

plotting 2

M333 - Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow

Model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   1691     2038.0                                
## 2   1690     1822.6  1  215.4  199.74 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 6585.713
## 2     2 6398.480
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * 
##     (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau   -0.33295    0.64045  -0.520    0.603    
## alpha  0.85976    0.05366  16.022  < 2e-16 ***
## A      5.78213    0.89533   6.458 1.38e-10 ***
## k     61.15069    6.48496   9.430  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.038 on 1690 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 9.562e-06
##   (59 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

Model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "a", "_MBg5", sep = "")), data = G_M333,  : 
##   parameters without starting value in 'data': tau
## Error in nls(get(paste("fg_", Mod.Sel1, "b", "_MBg5", sep = "")), data = G_M333,  : 
##   parameters without starting value in 'data': tau
## Error in nls(get(paste("fg_", Mod.Sel1, "c", "_MBg5", sep = "")), data = G_M333,  : 
##   parameters without starting value in 'data': tau
##   model     AIC
## 1     2 6398.48
## 2    2a      NA
## 3    2b      NA
## 4    2c      NA
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * 
##     (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau   -0.33295    0.64045  -0.520    0.603    
## alpha  0.85976    0.05366  16.022  < 2e-16 ***
## A      5.78213    0.89533   6.458 1.38e-10 ***
## k     61.15069    6.48496   9.430  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.038 on 1690 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 9.562e-06
##   (59 observations deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.92681, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -5.6822, p-value = 1.329e-08
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 29 rows containing missing values (`geom_point()`).
## Warning: Removed 925 rows containing missing values (`geom_line()`).

plotting 2

M334 - Black Hills Coniferous Forest

Model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1    355     329.22                                
## 2    354     306.86  1 22.366  25.802 6.132e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 1055.669
## 2     2 1032.482
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * 
##     (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    -0.7785     0.8475  -0.919  0.35894    
## alpha   0.7622     0.1330   5.731 2.14e-08 ***
## A       2.9995     0.6721   4.463 1.09e-05 ***
## k      37.6314    11.3745   3.308  0.00103 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.931 on 354 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 2.618e-06
##   (101 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

Model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "a", "_MBg5", sep = "")), data = G_M334,  : 
##   parameters without starting value in 'data': tau
## Error in nls(get(paste("fg_", Mod.Sel1, "b", "_MBg5", sep = "")), data = G_M334,  : 
##   parameters without starting value in 'data': tau
## Error in nls(get(paste("fg_", Mod.Sel1, "c", "_MBg5", sep = "")), data = G_M334,  : 
##   parameters without starting value in 'data': tau
##   model      AIC
## 1     2 1032.482
## 2    2a       NA
## 3    2b       NA
## 4    2c       NA
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * 
##     (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    -0.7785     0.8475  -0.919  0.35894    
## alpha   0.7622     0.1330   5.731 2.14e-08 ***
## A       2.9995     0.6721   4.463 1.09e-05 ***
## k      37.6314    11.3745   3.308  0.00103 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.931 on 354 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 2.618e-06
##   (101 observations deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.82141, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -1.998, p-value = 0.04572
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 48 rows containing missing values (`geom_point()`).
## Warning: Removed 1264 rows containing missing values (`geom_line()`).

plotting 2

M341 - Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow

Model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

Model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2


Fitted parameters

Best / selected models by ecoprovince

Code Ecoregion Sel.Mod
211 Northeastern Mixed Forest 2
212 Laurentian Mixed Forest 2
221 Eastern Broadleaf Forest 2
222 Midwest Broadleaf Forest 2
223 Central Interior Broadleaf Forest 2
231 Southeastern Mixed Forest 2
232 Outer Coastal Plain Mixed Forest 2
234 Lower Mississippi Riverine Forest 2
242 Pacific Lowland Mixed Forest 2
251 Prairie Parkland (Temperate) 1
255 Prairie Parkland (Subtropical) NA
261 California Coastal Chaparral Forest and Shrub NA
262 California Dry Steppe NA
263 California Coastal Steppe - Mixed Forest and Redwood Forest NA
313 Colorado Plateau Semi-Desert 2
315 Southwest Plateau and Plains Dry Steppe and Shrub NA
321 Chihuahuan Semi-Desert NA
322 American Semidesert and Desert NA
331 Great Plains/Palouse Dry Steppe NA
332 Great Plains Steppe 1
341 Intermountain Semi-Desert and Desert NA
342 Intermountain Semi-Desert 2
411 Everglades NA
M211 Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow 2
M221 Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow 2
M223 Ozark Broadleaf Forest Meadow 2
M231 Ouachita Mixed Forest 2
M242 Cascade Mixed Forest 2
M261 Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow 2
M262 California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow NA
M313 Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow 2
M331 Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow 2
M332 Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow 2
M333 Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow 2
M334 Black Hills Coniferous Forest 2
M341 Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow NA

table by ecoprovince

Code Ecoregion region n.obs n.plots tau tau.variance tau.2.5 tau.97.5 alpha alpha.variance alpha.2.5 alpha.97.5 A A.2.5 A.97.5 k k.2.5 k.97.5
211 Northeastern Mixed Forest east 6877 2876 1.0226050 0.0519878 0.5756375 1.4695724 0.1514785 0.0014519 0.0767828 0.2261741 3.587040 3.2949297 3.879151 32.13641 28.711930 35.56088
212 Laurentian Mixed Forest east 22715 9499 1.3387330 0.0335010 0.9799723 1.6974936 0.2731086 0.0006585 0.2228094 0.3234078 3.215390 3.0216746 3.409105 43.84726 40.923499 46.77103
221 Eastern Broadleaf Forest east 7333 3571 -0.8602079 0.0142148 -1.0939255 -0.6264904 0.5232389 0.0015948 0.4449551 0.6015226 5.932320 5.5348903 6.329749 32.54201 27.493976 37.59004
222 Midwest Broadleaf Forest east 5845 2589 0.0603405 0.0465895 -0.3628157 0.4834966 0.4289446 0.0022828 0.3352762 0.5226130 5.056391 4.5882249 5.524558 41.09173 35.653746 46.52972
223 Central Interior Broadleaf Forest east 10010 3864 -0.8121234 0.0116899 -1.0240639 -0.6001829 0.4738433 0.0016610 0.3939523 0.5537342 6.293537 5.8499174 6.737157 62.38730 54.144505 70.63010
231 Southeastern Mixed Forest east 13517 6193 2.0510032 0.0476053 1.6233265 2.4786798 0.5782563 0.0004673 0.5358818 0.6206308 4.039289 3.7841680 4.294410 12.85831 11.422197 14.29443
232 Outer Coastal Plain Mixed Forest east 13629 6626 1.2829040 0.0380496 0.9005528 1.6652552 0.5530174 0.0004686 0.5105848 0.5954501 4.565889 4.2666295 4.865149 19.58218 17.626745 21.53761
234 Lower Mississippi Riverine Forest east 1388 778 1.3876959 0.8084870 -0.3762372 3.1516290 0.7200306 0.0071467 0.5541876 0.8858735 4.090264 2.8796789 5.300849 12.26760 6.527838 18.00737
242 Pacific Lowland Mixed Forest pacific 83 83 -0.1711992 6.2989162 -5.1698277 4.8274294 0.8912680 0.1256302 0.1853325 1.5972035 8.538822 -0.7741012 17.851745 29.06994 -1.749796 59.88967
251 Prairie Parkland (Temperate) east 2295 906 0.4526785 0.2446043 -0.5173282 1.4226853 NA NA NA NA 3.470867 2.8002520 4.141481 24.05661 15.690636 32.42259
255 Prairie Parkland (Subtropical) east 717 319 NA NA NA NA NA NA NA NA NA NA NA NA NA NA
261 California Coastal Chaparral Forest and Shrub pacific 25 25 NA NA NA NA NA NA NA NA NA NA NA NA NA NA
262 California Dry Steppe pacific 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA
263 California Coastal Steppe - Mixed Forest and Redwood Forest pacific 163 161 NA NA NA NA NA NA NA NA NA NA NA NA NA NA
313 Colorado Plateau Semi-Desert interior west 218 218 -1.2288065 0.8037346 -2.9960752 0.5384623 0.7286917 0.0611899 0.2410667 1.2163167 4.567967 1.7131691 7.422764 120.25652 45.885956 194.62709
315 Southwest Plateau and Plains Dry Steppe and Shrub interior west 4 4 NA NA NA NA NA NA NA NA NA NA NA NA NA NA
321 Chihuahuan Semi-Desert interior west 9 9 NA NA NA NA NA NA NA NA NA NA NA NA NA NA
322 American Semidesert and Desert interior west 3 3 NA NA NA NA NA NA NA NA NA NA NA NA NA NA
331 Great Plains/Palouse Dry Steppe interior west 331 255 NA NA NA NA NA NA NA NA NA NA NA NA NA NA
332 Great Plains Steppe interior west 232 128 0.3290914 1.8705883 -2.3684559 3.0266386 NA NA NA NA 4.342163 1.7462960 6.938029 74.75556 28.375089 121.13604
341 Intermountain Semi-Desert and Desert interior west 66 64 NA NA NA NA NA NA NA NA NA NA NA NA NA NA
342 Intermountain Semi-Desert interior west 124 123 2.8735167 43.4175637 -10.1834240 15.9304575 0.8880369 0.0552257 0.4223658 1.3537080 2.919332 -2.1263725 7.965035 90.85407 23.015368 158.69278
411 Everglades east 96 63 NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M211 Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow east 6772 3006 1.7786421 0.0838090 1.2111348 2.3461494 0.2035009 0.0010577 0.1397484 0.2672535 2.998289 2.7197370 3.276841 33.06165 29.592339 36.53096
M221 Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow east 8315 3810 0.0106157 0.0253307 -0.3013705 0.3226019 0.5678328 0.0030888 0.4588878 0.6767779 4.806111 4.4485294 5.163693 27.74238 22.287527 33.19724
M223 Ozark Broadleaf Forest Meadow east 896 349 2.3198982 1.5314664 -0.1089228 4.7487192 0.4618123 0.0255588 0.1480418 0.7755827 2.451102 1.5143755 3.387828 31.93472 11.953289 51.91616
M231 Ouachita Mixed Forest east 1006 495 3.6086566 3.1203260 0.1422427 7.0750706 0.3981807 0.0120643 0.1826393 0.6137221 2.359071 1.3174800 3.400662 34.12849 20.138981 48.11800
M242 Cascade Mixed Forest pacific 3224 3207 -1.6967250 0.0569485 -2.1646285 -1.2288214 0.9041933 0.0050426 0.7649596 1.0434271 13.038763 10.9107794 15.166746 140.11490 118.310628 161.91917
M261 Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow pacific 1977 1807 -1.5662388 0.1364314 -2.2907049 -0.8417727 0.6405465 0.0113330 0.4317453 0.8493478 15.152926 11.4986698 18.807181 247.12429 188.762394 305.48619
M262 California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow interior west 30 26 NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M313 Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow interior west 367 367 -2.1151193 0.1050385 -2.7524676 -1.4777710 0.5769339 0.0129929 0.3527748 0.8010930 9.051883 5.7957703 12.307996 153.81728 83.422344 224.21222
M331 Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow interior west 1756 1756 -0.7064804 0.3219889 -1.8194218 0.4064611 0.6126066 0.0030822 0.5037180 0.7214952 2.715381 1.9075824 3.523179 49.20052 34.913026 63.48802
M332 Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow interior west 2612 2602 -0.8597398 0.1744170 -1.6786792 -0.0408004 0.7796848 0.0024433 0.6827569 0.8766126 5.266247 4.0083136 6.524181 87.68462 69.726871 105.64238
M333 Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow interior west 1753 1742 -0.3329468 0.4101749 -1.5891034 0.9232097 0.8597628 0.0028795 0.7545146 0.9650110 5.782128 4.0260469 7.538210 61.15069 48.431305 73.87008
M334 Black Hills Coniferous Forest interior west 459 181 -0.7784535 0.7181787 -2.4451315 0.8882244 0.7621556 0.0176865 0.5006044 1.0237068 2.999537 1.6777117 4.321362 37.63137 15.261203 60.00153
M341 Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow interior west 220 220 NA NA NA NA NA NA NA NA NA NA NA NA NA NA

plot tau

map

## OGR data source with driver: ESRI Shapefile 
## Source: "C:\Users\hogan.jaaron\Dropbox\FIA_R\Mapping\S_USA.EcoMapProvinces\S_USA.EcoMapProvinces.shp", layer: "S_USA.EcoMapProvinces"
## with 37 features
## It has 17 fields
## Integer64 fields read as strings:  PROVINCE_ PROVINCE_I
## Warning: package 'ggnewscale' was built under R version 4.2.1
## Warning: `aes_string()` was deprecated in ggplot2 3.0.0.
## ℹ Please use tidy evaluation ideoms with `aes()`
## Warning: The `size` argument of `element_line()` is deprecated as of ggplot2 3.4.0.
## ℹ Please use the `linewidth` argument instead.
## Warning in grid.Call(C_stringMetric, as.graphicsAnnot(x$label)): font family not
## found in Windows font database

## Warning in grid.Call(C_stringMetric, as.graphicsAnnot(x$label)): font family not
## found in Windows font database
## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

plot alpha (biomass growth compensation effect)

plot A (asymptote of forest biomass growth in Mg/ha/yr)

## Warning: Removed 12 rows containing missing values (`geom_point()`).

plot k (stand biomass at half biomss G in Mg/ha)

## Warning: Removed 12 rows containing missing values (`geom_point()`).

Caclulations - weighted averages

tau (productivity trend (in %) 2000-2021)

##          region weighted.tau weighted.tau.std_Error 95 % CI, upper
## 1     entire US   0.46864470             0.06827335     0.60246046
## 2       pacific  -0.14304359             0.01789591    -0.10796761
## 3          east   0.69536681             0.05562962     0.80440087
## 4 interior west  -0.08367852             0.03530342    -0.01448381
##   95 % CI, lower
## 1      0.3348289
## 2     -0.1781196
## 3      0.5863327
## 4     -0.1528732

alpha (biomass growth compensation effect)

##          region weighted.alpha weighted.alpha.std_Error 95 % CI, upper
## 1     entire US     0.48562909             1.802426e-07     0.48562944
## 2       pacific     0.07131965             5.171433e-03     0.08145566
## 3          east     0.32419373             8.371647e-03     0.34060216
## 4 interior west     0.09011570             3.489543e-03     0.09695521
##   95 % CI, lower
## 1     0.48562873
## 2     0.06118364
## 3     0.30778530
## 4     0.08327620

A (asymptote of forest biomass growth in Mg/ha/yr)

##          region weighted.A
## 1     entire US   5.086239
## 2       pacific  13.232135
## 3          east   4.236292
## 4 interior west   4.458184

K (stand biomass at half biomass G in Mg/ha)

##          region weighted.k
## 1     entire US   49.65117
## 2       pacific  170.03878
## 3          east   32.18296
## 4 interior west   69.01766

Analaysis 2: \(G_{TI-NoIngrow}\)

211 - Northeastern Mixed Forest

Model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   6822     4506.3                                
## 2   6821     4178.5  1 327.82  535.14 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 21450.25
## 2     2 20936.76
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.55605    0.18380   3.025  0.00249 ** 
## alpha   0.79613    0.03177  25.061  < 2e-16 ***
## A       4.92563    0.20624  23.884  < 2e-16 ***
## k     113.43273    5.37133  21.118  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7827 on 6821 degrees of freedom
## 
## Number of iterations to convergence: 4 
## Achieved convergence tolerance: 5.58e-06
##   (52 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

Model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "a", "_TI", sep = "")), data = G_211,  : 
##   parameters without starting value in 'data': tau, phi, DeltaPDSI
## Error in nls(get(paste("fg_", Mod.Sel1, "b", "_TI", sep = "")), data = G_211,  : 
##   parameters without starting value in 'data': tau, phi, DeltaPDSI
## Error in nls(get(paste("fg_", Mod.Sel1, "c", "_TI", sep = "")), data = G_211,  : 
##   parameters without starting value in 'data': tau, phi, DeltaPDSI
##   model      AIC
## 1     2 20936.76
## 2    2a       NA
## 3    2b       NA
## 4    2c       NA
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.55605    0.18380   3.025  0.00249 ** 
## alpha   0.79613    0.03177  25.061  < 2e-16 ***
## A       4.92563    0.20624  23.884  < 2e-16 ***
## k     113.43273    5.37133  21.118  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7827 on 6821 degrees of freedom
## 
## Number of iterations to convergence: 4 
## Achieved convergence tolerance: 5.58e-06
##   (52 observations deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

predict and plot

## Warning: Removed 22 rows containing missing values (`geom_point()`).
## Warning: Removed 1038 rows containing missing values (`geom_line()`).

plotting 2

212 - Laurentian Mixed Forest

Model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1  18911      11656                                
## 2  18910      10322  1 1333.6  2443.1 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 47432.75
## 2     2 45136.56
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     1.15700    0.15150   7.637 2.33e-14 ***
## alpha   1.06939    0.01945  54.995  < 2e-16 ***
## A       5.57364    0.19898  28.012  < 2e-16 ***
## k     213.12553    8.12030  26.246  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7388 on 18910 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 2.389e-06
##   (3801 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

Model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "a", "_TI", sep = "")), data = G_212,  : 
##   parameters without starting value in 'data': tau, phi, DeltaPDSI
## Error in nls(get(paste("fg_", Mod.Sel1, "b", "_TI", sep = "")), data = G_212,  : 
##   parameters without starting value in 'data': tau, phi, DeltaPDSI
## Error in nls(get(paste("fg_", Mod.Sel1, "c", "_TI", sep = "")), data = G_212,  : 
##   parameters without starting value in 'data': tau, phi, DeltaPDSI
##   model      AIC
## 1     2 45136.56
## 2    2a       NA
## 3    2b       NA
## 4    2c       NA
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     1.15700    0.15150   7.637 2.33e-14 ***
## alpha   1.06939    0.01945  54.995  < 2e-16 ***
## A       5.57364    0.19898  28.012  < 2e-16 ***
## k     213.12553    8.12030  26.246  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7388 on 18910 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 2.389e-06
##   (3801 observations deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

predict and plot

## Warning: Removed 1880 rows containing missing values (`geom_point()`).
## Warning: Removed 1031 rows containing missing values (`geom_line()`).

plotting 2

221 - Eastern Broadleaf Forest

Model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   7266     7882.2                                
## 2   7265     7425.5  1  456.7  446.83 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 28950.11
## 2     2 28518.25
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau   -0.93025    0.11070  -8.404   <2e-16 ***
## alpha  0.82261    0.03629  22.666   <2e-16 ***
## A      7.02241    0.27128  25.886   <2e-16 ***
## k     89.63813    5.69014  15.753   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.011 on 7265 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 8.389e-06
##   (64 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

Model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "a", "_TI", sep = "")), data = G_221,  : 
##   parameters without starting value in 'data': tau, phi, DeltaPDSI
## Error in nls(get(paste("fg_", Mod.Sel1, "b", "_TI", sep = "")), data = G_221,  : 
##   parameters without starting value in 'data': tau, phi, DeltaPDSI
## Error in nls(get(paste("fg_", Mod.Sel1, "c", "_TI", sep = "")), data = G_221,  : 
##   parameters without starting value in 'data': tau, phi, DeltaPDSI
##   model      AIC
## 1     2 28518.25
## 2    2a       NA
## 3    2b       NA
## 4    2c       NA
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau   -0.93025    0.11070  -8.404   <2e-16 ***
## alpha  0.82261    0.03629  22.666   <2e-16 ***
## A      7.02241    0.27128  25.886   <2e-16 ***
## k     89.63813    5.69014  15.753   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.011 on 7265 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 8.389e-06
##   (64 observations deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

predict and plot

## Warning: Removed 29 rows containing missing values (`geom_point()`).
## Warning: Removed 1036 rows containing missing values (`geom_line()`).

plotting 2

222 - Midwest Broadleaf Forest

Model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   4839     3647.5                                
## 2   4838     3294.3  1 353.26   518.8 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 15860.31
## 2     2 15369.08
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau     0.2268     0.2059   1.102    0.271    
## alpha   0.9716     0.0384  25.303   <2e-16 ***
## A       6.8417     0.3634  18.829   <2e-16 ***
## k     141.3510     8.6834  16.278   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8252 on 4838 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 6.595e-07
##   (1003 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

Model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "a", "_TI", sep = "")), data = G_222,  : 
##   parameters without starting value in 'data': tau, phi, DeltaPDSI
## Error in nls(get(paste("fg_", Mod.Sel1, "b", "_TI", sep = "")), data = G_222,  : 
##   parameters without starting value in 'data': tau, phi, DeltaPDSI
## Error in nls(get(paste("fg_", Mod.Sel1, "c", "_TI", sep = "")), data = G_222,  : 
##   parameters without starting value in 'data': tau, phi, DeltaPDSI
##   model      AIC
## 1     2 15369.08
## 2    2a       NA
## 3    2b       NA
## 4    2c       NA
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau     0.2268     0.2059   1.102    0.271    
## alpha   0.9716     0.0384  25.303   <2e-16 ***
## A       6.8417     0.3634  18.829   <2e-16 ***
## k     141.3510     8.6834  16.278   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8252 on 4838 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 6.595e-07
##   (1003 observations deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

predict and plot

## Warning: Removed 530 rows containing missing values (`geom_point()`).
## Warning: Removed 1053 rows containing missing values (`geom_line()`).

plotting 2

223 - Central Interior Broadleaf Forest

Model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   8742     7835.7                                
## 2   8741     7412.5  1 423.24  499.09 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 31017.79
## 2     2 30534.21
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau    -0.98667    0.09422  -10.47   <2e-16 ***
## alpha   0.84872    0.03506   24.21   <2e-16 ***
## A      11.86883    0.67873   17.49   <2e-16 ***
## k     263.34595   19.70084   13.37   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9209 on 8741 degrees of freedom
## 
## Number of iterations to convergence: 9 
## Achieved convergence tolerance: 2.834e-06
##   (1265 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

Model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "a", "_TI", sep = "")), data = G_223,  : 
##   parameters without starting value in 'data': tau, phi, DeltaPDSI
## Error in nls(get(paste("fg_", Mod.Sel1, "b", "_TI", sep = "")), data = G_223,  : 
##   parameters without starting value in 'data': tau, phi, DeltaPDSI
## Error in nls(get(paste("fg_", Mod.Sel1, "c", "_TI", sep = "")), data = G_223,  : 
##   parameters without starting value in 'data': tau, phi, DeltaPDSI
##   model      AIC
## 1     2 30534.21
## 2    2a       NA
## 3    2b       NA
## 4    2c       NA
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau    -0.98667    0.09422  -10.47   <2e-16 ***
## alpha   0.84872    0.03506   24.21   <2e-16 ***
## A      11.86883    0.67873   17.49   <2e-16 ***
## k     263.34595   19.70084   13.37   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9209 on 8741 degrees of freedom
## 
## Number of iterations to convergence: 9 
## Achieved convergence tolerance: 2.834e-06
##   (1265 observations deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

predict and plot

## Warning: Removed 628 rows containing missing values (`geom_point()`).
## Warning: Removed 1002 rows containing missing values (`geom_line()`).

plotting 2

231 - Southeastern Mixed Forest

Model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1  13233      26261                                
## 2  13232      23406  1 2855.4  1614.2 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 60936.50
## 2     2 59414.92
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    1.55319    0.19646   7.906 2.87e-15 ***
## alpha  0.93883    0.02094  44.825  < 2e-16 ***
## A      5.08782    0.17961  28.327  < 2e-16 ***
## k     62.69065    2.80418  22.356  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.33 on 13232 degrees of freedom
## 
## Number of iterations to convergence: 4 
## Achieved convergence tolerance: 5.568e-06
##   (281 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

Model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "a", "_TI", sep = "")), data = G_231,  : 
##   parameters without starting value in 'data': tau, phi, DeltaPDSI
## Error in nls(get(paste("fg_", Mod.Sel1, "b", "_TI", sep = "")), data = G_231,  : 
##   parameters without starting value in 'data': tau, phi, DeltaPDSI
## Error in nls(get(paste("fg_", Mod.Sel1, "c", "_TI", sep = "")), data = G_231,  : 
##   parameters without starting value in 'data': tau, phi, DeltaPDSI
##   model      AIC
## 1     2 59414.92
## 2    2a       NA
## 3    2b       NA
## 4    2c       NA
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    1.55319    0.19646   7.906 2.87e-15 ***
## alpha  0.93883    0.02094  44.825  < 2e-16 ***
## A      5.08782    0.17961  28.327  < 2e-16 ***
## k     62.69065    2.80418  22.356  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.33 on 13232 degrees of freedom
## 
## Number of iterations to convergence: 4 
## Achieved convergence tolerance: 5.568e-06
##   (281 observations deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

predict and plot

## Warning: Removed 139 rows containing missing values (`geom_point()`).
## Warning: Removed 1017 rows containing missing values (`geom_line()`).

plotting 2

232 - Outer Coastal Plain Mixed Forest

Model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1  13303      28896                                
## 2  13302      25620  1 3276.2    1701 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 60049.81
## 2     2 58450.60
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    1.10660    0.19007   5.822 5.95e-09 ***
## alpha  0.96245    0.02054  46.846  < 2e-16 ***
## A      5.28979    0.19504  27.121  < 2e-16 ***
## k     68.64871    3.00260  22.863  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.388 on 13302 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 9.537e-07
##   (323 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

Model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "a", "_TI", sep = "")), data = G_232,  : 
##   parameters without starting value in 'data': tau, phi, DeltaPDSI
## Error in nls(get(paste("fg_", Mod.Sel1, "b", "_TI", sep = "")), data = G_232,  : 
##   parameters without starting value in 'data': tau, phi, DeltaPDSI
## Error in nls(get(paste("fg_", Mod.Sel1, "c", "_TI", sep = "")), data = G_232,  : 
##   parameters without starting value in 'data': tau, phi, DeltaPDSI
##   model     AIC
## 1     2 58450.6
## 2    2a      NA
## 3    2b      NA
## 4    2c      NA
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    1.10660    0.19007   5.822 5.95e-09 ***
## alpha  0.96245    0.02054  46.846  < 2e-16 ***
## A      5.28979    0.19504  27.121  < 2e-16 ***
## k     68.64871    3.00260  22.863  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.388 on 13302 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 9.537e-07
##   (323 observations deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

predict and plot

## Warning: Removed 178 rows containing missing values (`geom_point()`).
## Warning: Removed 931 rows containing missing values (`geom_line()`).

plotting 2

234 - Lower Mississippi Riverine Forest

Model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   1324     3905.3                                
## 2   1323     3650.9  1 254.34  92.167 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 6664.563
## 2     2 6577.195
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    2.21590    1.31257   1.688   0.0916 .  
## alpha  0.98846    0.09115  10.845  < 2e-16 ***
## A      4.12529    0.82457   5.003 6.40e-07 ***
## k     56.92517   10.41403   5.466 5.49e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.661 on 1323 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 4.056e-07
##   (61 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

Model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "a", "_TI", sep = "")), data = G_234,  : 
##   parameters without starting value in 'data': tau, phi, DeltaPDSI
## Error in nls(get(paste("fg_", Mod.Sel1, "b", "_TI", sep = "")), data = G_234,  : 
##   parameters without starting value in 'data': tau, phi, DeltaPDSI
## Error in nls(get(paste("fg_", Mod.Sel1, "c", "_TI", sep = "")), data = G_234,  : 
##   parameters without starting value in 'data': tau, phi, DeltaPDSI
##   model      AIC
## 1     2 6577.195
## 2    2a       NA
## 3    2b       NA
## 4    2c       NA
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    2.21590    1.31257   1.688   0.0916 .  
## alpha  0.98846    0.09115  10.845  < 2e-16 ***
## A      4.12529    0.82457   5.003 6.40e-07 ***
## k     56.92517   10.41403   5.466 5.49e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.661 on 1323 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 4.056e-07
##   (61 observations deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.84539, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -3.2555, p-value = 0.001132
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 31 rows containing missing values (`geom_point()`).
## Warning: Removed 645 rows containing missing values (`geom_line()`).

plotting 2

242 - Pacific Lowland Mixed Forest

Model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value  Pr(>F)  
## 1     77     64.151                            
## 2     76     59.090  1 5.0607   6.509 0.01274 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 340.6367
## 2     2 336.0628
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)   
## tau     1.6580     3.7292   0.445  0.65787   
## alpha   0.7566     0.2720   2.782  0.00682 **
## A       6.2469     3.6800   1.698  0.09368 . 
## k      90.6221    27.7195   3.269  0.00162 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8818 on 76 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 1.05e-06
##   (3 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

Model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "a", "_TI", sep = "")), data = G_242,  : 
##   parameters without starting value in 'data': tau, phi, DeltaPDSI
## Error in nls(get(paste("fg_", Mod.Sel1, "b", "_TI", sep = "")), data = G_242,  : 
##   parameters without starting value in 'data': tau, phi, DeltaPDSI
## Error in nls(get(paste("fg_", Mod.Sel1, "c", "_TI", sep = "")), data = G_242,  : 
##   parameters without starting value in 'data': tau, phi, DeltaPDSI
##   model      AIC
## 1     2 336.0628
## 2    2a       NA
## 3    2b       NA
## 4    2c       NA
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)   
## tau     1.6580     3.7292   0.445  0.65787   
## alpha   0.7566     0.2720   2.782  0.00682 **
## A       6.2469     3.6800   1.698  0.09368 . 
## k      90.6221    27.7195   3.269  0.00162 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8818 on 76 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 1.05e-06
##   (3 observations deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.98469, p-value = 0.4569
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = 0.14291, p-value = 0.8864
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 1 rows containing missing values (`geom_point()`).
## Warning: Removed 725 rows containing missing values (`geom_line()`).

plotting 2

251 - Prairie Parkland (Temperate)

Model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   1785     1329.7                                
## 2   1784     1305.5  1 24.104  32.937 1.116e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 5834.037
## 2     2 5803.328
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    0.68113    0.42631   1.598     0.11    
## alpha  0.54867    0.09052   6.062 1.64e-09 ***
## A      4.54602    0.44240  10.276  < 2e-16 ***
## k     98.08080   11.90142   8.241 3.27e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8555 on 1784 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 4.188e-06
##   (507 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

Model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "a", "_TI", sep = "")), data = G_251,  : 
##   parameters without starting value in 'data': tau, phi, DeltaPDSI
## Error in nls(get(paste("fg_", Mod.Sel1, "b", "_TI", sep = "")), data = G_251,  : 
##   parameters without starting value in 'data': tau, phi, DeltaPDSI
## Error in nls(get(paste("fg_", Mod.Sel1, "c", "_TI", sep = "")), data = G_251,  : 
##   parameters without starting value in 'data': tau, phi, DeltaPDSI
##   model      AIC
## 1     2 5803.328
## 2    2a       NA
## 3    2b       NA
## 4    2c       NA
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    0.68113    0.42631   1.598     0.11    
## alpha  0.54867    0.09052   6.062 1.64e-09 ***
## A      4.54602    0.44240  10.276  < 2e-16 ***
## k     98.08080   11.90142   8.241 3.27e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8555 on 1784 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 4.188e-06
##   (507 observations deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.88257, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -8.7257, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 276 rows containing missing values (`geom_point()`).
## Warning: Removed 1176 rows containing missing values (`geom_line()`).

plotting 2

255 - Prairie Parkland (Subtropical)

Model selection 1

## Error in nls(fg_1_TI, data = G_255, start = c(tau = tau.start, A = A.start,  : 
##   number of iterations exceeded maximum of 50
## Error in nls(fg_2_TI, data = G_255, start = c(tau = tau.start, alpha = alpha.start,  : 
##   number of iterations exceeded maximum of 50
##   model AIC
## 1     1  NA
## 2     2  NA
## Warning in min(AIC1_255$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in h(simpleError(msg, call)) : 
##   error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_255.' not found

summary

  • simple model: does not fit
  • alpha model: does not fit

Model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

261 - California Coastal Chaparral Forest and Shrub

Model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

Model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

262 - California Dry Steppe

Model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

Model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

263 - California Coastal Steppe - Mixed Forest and Redwood Forest

Model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

Model selection 2

summary

  • add p model: does not fit

  • add s model: does not fit

  • add s+p model: does not fit

  • note: model fit, but fit was funky due to data being sparse

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

313 - Colorado Plateau Semi-Desert

Model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1    212     92.785                                
## 2    211     87.782  1 5.0027  12.025 0.0006362 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 433.8518
## 2     2 423.9356
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    -0.7114     1.2406  -0.573  0.56699    
## alpha   0.9558     0.2401   3.981 9.45e-05 ***
## A       4.5484     1.7705   2.569  0.01089 *  
## k     189.5822    67.5160   2.808  0.00545 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.645 on 211 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 8.574e-06
##   (3 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

Model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "a", "_TI", sep = "")), data = G_313,  : 
##   parameters without starting value in 'data': tau, phi, DeltaPDSI
## Error in nls(get(paste("fg_", Mod.Sel1, "b", "_TI", sep = "")), data = G_313,  : 
##   parameters without starting value in 'data': tau, phi, DeltaPDSI
## Error in nls(get(paste("fg_", Mod.Sel1, "c", "_TI", sep = "")), data = G_313,  : 
##   parameters without starting value in 'data': tau, phi, DeltaPDSI
##   model      AIC
## 1     2 423.9356
## 2    2a       NA
## 3    2b       NA
## 4    2c       NA
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    -0.7114     1.2406  -0.573  0.56699    
## alpha   0.9558     0.2401   3.981 9.45e-05 ***
## A       4.5484     1.7705   2.569  0.01089 *  
## k     189.5822    67.5160   2.808  0.00545 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.645 on 211 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 8.574e-06
##   (3 observations deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.98376, p-value = 0.01428
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = 0.18459, p-value = 0.8536
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 1 rows containing missing values (`geom_point()`).
## Warning: Removed 1103 rows containing missing values (`geom_line()`).

plotting 2

315 - Southwest Plateau and Plains Dry Steppe and Shrub

Model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

Model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

321 - Chihuahuan Semi-Desert

Model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

Model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

322 - American Semidesert and Desert

Model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

Model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

331 - Great Plains/Palouse Dry Steppe

Model selection 1

## Error in nls(fg_1_TI, data = G_331, start = c(tau = tau.start, A = A.start,  : 
##   number of iterations exceeded maximum of 50
## Error in nls(fg_2_TI, data = G_331, start = c(tau = tau.start, alpha = alpha.start,  : 
##   number of iterations exceeded maximum of 50
##   model AIC
## 1     1  NA
## 2     2  NA
## Warning in min(AIC1_331$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in h(simpleError(msg, call)) : 
##   error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_331.' not found

summary

  • simple model: does not fit
  • alpha model: does not fit

Model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

332 - Great Plains Steppe

Model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value   Pr(>F)   
## 1    193     138.02                              
## 2    192     132.25  1 5.7715  8.3793 0.004235 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 536.3344
## 2     2 529.9619
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)   
## tau     1.7278     2.2867   0.756  0.45083   
## alpha   0.7986     0.2488   3.210  0.00156 **
## A       4.2036     1.6950   2.480  0.01400 * 
## k     144.4134    49.0241   2.946  0.00362 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8299 on 192 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 3.776e-06
##   (36 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

Model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "a", "_TI", sep = "")), data = G_332,  : 
##   parameters without starting value in 'data': tau, phi, DeltaPDSI
## Error in nls(get(paste("fg_", Mod.Sel1, "b", "_TI", sep = "")), data = G_332,  : 
##   parameters without starting value in 'data': tau, phi, DeltaPDSI
## Error in nls(get(paste("fg_", Mod.Sel1, "c", "_TI", sep = "")), data = G_332,  : 
##   parameters without starting value in 'data': tau, phi, DeltaPDSI
##   model      AIC
## 1     2 529.9619
## 2    2a       NA
## 3    2b       NA
## 4    2c       NA
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)   
## tau     1.7278     2.2867   0.756  0.45083   
## alpha   0.7986     0.2488   3.210  0.00156 **
## A       4.2036     1.6950   2.480  0.01400 * 
## k     144.4134    49.0241   2.946  0.00362 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8299 on 192 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 3.776e-06
##   (36 observations deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.81834, p-value = 2.286e-14
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -2.666, p-value = 0.007676
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 14 rows containing missing values (`geom_point()`).
## Warning: Removed 1120 rows containing missing values (`geom_line()`).

plotting 2

341 - Intermountain Semi-desert & Desert

Model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

Model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

342 - Intermountain Semi-Desert

Model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1    112     56.909                                
## 2    111     48.388  1 8.5209  19.547 2.299e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 240.3323
## 2     2 223.6793
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau     1.0857     3.4942   0.311   0.7566    
## alpha   1.0513     0.2047   5.135 1.22e-06 ***
## A       5.1810     3.3797   1.533   0.1281    
## k     176.6826    71.2802   2.479   0.0147 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6602 on 111 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 9.638e-06
##   (9 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

Model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "a", "_TI", sep = "")), data = G_342,  : 
##   parameters without starting value in 'data': tau, phi, DeltaPDSI
## Error in nls(get(paste("fg_", Mod.Sel1, "b", "_TI", sep = "")), data = G_342,  : 
##   parameters without starting value in 'data': tau, phi, DeltaPDSI
## Error in nls(get(paste("fg_", Mod.Sel1, "c", "_TI", sep = "")), data = G_342,  : 
##   parameters without starting value in 'data': tau, phi, DeltaPDSI
##   model      AIC
## 1     2 223.6793
## 2    2a       NA
## 3    2b       NA
## 4    2c       NA
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau     1.0857     3.4942   0.311   0.7566    
## alpha   1.0513     0.2047   5.135 1.22e-06 ***
## A       5.1810     3.3797   1.533   0.1281    
## k     176.6826    71.2802   2.479   0.0147 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6602 on 111 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 9.638e-06
##   (9 observations deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.90944, p-value = 9.729e-07
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -1.2102, p-value = 0.2262
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 5 rows containing missing values (`geom_point()`).
## Warning: Removed 1241 rows containing missing values (`geom_line()`).

plotting 2

411 - Everglades

Model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

Model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M211 - Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow

Model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   6746     4413.5                                
## 2   6745     4037.5  1    376  628.14 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 20675.75
## 2     2 20076.80
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     1.37896    0.26771   5.151 2.67e-07 ***
## alpha   0.81396    0.02971  27.393  < 2e-16 ***
## A       3.71986    0.19227  19.347  < 2e-16 ***
## k     104.43455    5.37051  19.446  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7737 on 6745 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 2.142e-06
##   (23 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

Model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "a", "_TI", sep = "")), data = G_M211,  : 
##   parameters without starting value in 'data': tau, phi, DeltaPDSI
## Error in nls(get(paste("fg_", Mod.Sel1, "b", "_TI", sep = "")), data = G_M211,  : 
##   parameters without starting value in 'data': tau, phi, DeltaPDSI
## Error in nls(get(paste("fg_", Mod.Sel1, "c", "_TI", sep = "")), data = G_M211,  : 
##   parameters without starting value in 'data': tau, phi, DeltaPDSI
##   model     AIC
## 1     2 20076.8
## 2    2a      NA
## 3    2b      NA
## 4    2c      NA
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     1.37896    0.26771   5.151 2.67e-07 ***
## alpha   0.81396    0.02971  27.393  < 2e-16 ***
## A       3.71986    0.19227  19.347  < 2e-16 ***
## k     104.43455    5.37051  19.446  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7737 on 6745 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 2.142e-06
##   (23 observations deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

predict and plot

## Warning: Removed 15 rows containing missing values (`geom_point()`).
## Warning: Removed 1108 rows containing missing values (`geom_line()`).

plotting 2

M221 - Eastern Broadleaf Forest

Model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   8257      12696                                
## 2   8256      12324  1 371.97  249.19 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 36024.31
## 2     2 35780.69
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.31033    0.17766   1.747   0.0807 .  
## alpha   0.88596    0.05292  16.743   <2e-16 ***
## A       5.64956    0.27514  20.533   <2e-16 ***
## k     105.48995    7.91642  13.325   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.222 on 8256 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 1.972e-06
##   (55 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

Model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "a", "_TI", sep = "")), data = G_M221,  : 
##   parameters without starting value in 'data': tau, phi, DeltaPDSI
## Error in nls(get(paste("fg_", Mod.Sel1, "b", "_TI", sep = "")), data = G_M221,  : 
##   parameters without starting value in 'data': tau, phi, DeltaPDSI
## Error in nls(get(paste("fg_", Mod.Sel1, "c", "_TI", sep = "")), data = G_M221,  : 
##   parameters without starting value in 'data': tau, phi, DeltaPDSI
##   model      AIC
## 1     2 35780.69
## 2    2a       NA
## 3    2b       NA
## 4    2c       NA
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.31033    0.17766   1.747   0.0807 .  
## alpha   0.88596    0.05292  16.743   <2e-16 ***
## A       5.64956    0.27514  20.533   <2e-16 ***
## k     105.48995    7.91642  13.325   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.222 on 8256 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 1.972e-06
##   (55 observations deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

predict and plot

## Warning: Removed 22 rows containing missing values (`geom_point()`).
## Warning: Removed 982 rows containing missing values (`geom_line()`).

plotting 2

M223 - Ozark Broadleaf Forest Meadow

Model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1    887     1168.5                                
## 2    886     1122.8  1 45.629  36.005 2.866e-09 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 3366.802
## 2     2 3333.350
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau     3.5517     1.8231   1.948 0.051715 .  
## alpha   1.0187     0.1552   6.563 8.95e-11 ***
## A       2.7562     0.7427   3.711 0.000219 ***
## k     114.7022    32.6123   3.517 0.000458 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.126 on 886 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 4.074e-06
##   (6 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

Model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "a", "_TI", sep = "")), data = G_M223,  : 
##   parameters without starting value in 'data': tau, phi, DeltaPDSI
## Error in nls(get(paste("fg_", Mod.Sel1, "b", "_TI", sep = "")), data = G_M223,  : 
##   parameters without starting value in 'data': tau, phi, DeltaPDSI
## Error in nls(get(paste("fg_", Mod.Sel1, "c", "_TI", sep = "")), data = G_M223,  : 
##   parameters without starting value in 'data': tau, phi, DeltaPDSI
##   model     AIC
## 1     2 3333.35
## 2    2a      NA
## 3    2b      NA
## 4    2c      NA
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau     3.5517     1.8231   1.948 0.051715 .  
## alpha   1.0187     0.1552   6.563 8.95e-11 ***
## A       2.7562     0.7427   3.711 0.000219 ***
## k     114.7022    32.6123   3.517 0.000458 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.126 on 886 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 4.074e-06
##   (6 observations deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.95654, p-value = 1.414e-15
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -1.0727, p-value = 0.2834
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 4 rows containing missing values (`geom_point()`).
## Warning: Removed 1175 rows containing missing values (`geom_line()`).

plotting 2

M231 - Ouachita Mixed Forest

Model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1    989     1289.9                                
## 2    988     1209.2  1 80.707  65.945 1.373e-15 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 3745.090
## 2     2 3682.993
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau     5.0159     2.5882   1.938 0.052908 .  
## alpha   0.9369     0.1062   8.821  < 2e-16 ***
## A       2.7200     0.8084   3.365 0.000796 ***
## k     114.4827    24.7841   4.619 4.36e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.106 on 988 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 2.507e-06
##   (14 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

Model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "a", "_TI", sep = "")), data = G_M231,  : 
##   parameters without starting value in 'data': tau, phi, DeltaPDSI
## Error in nls(get(paste("fg_", Mod.Sel1, "b", "_TI", sep = "")), data = G_M231,  : 
##   parameters without starting value in 'data': tau, phi, DeltaPDSI
## Error in nls(get(paste("fg_", Mod.Sel1, "c", "_TI", sep = "")), data = G_M231,  : 
##   parameters without starting value in 'data': tau, phi, DeltaPDSI
##   model      AIC
## 1     2 3682.993
## 2    2a       NA
## 3    2b       NA
## 4    2c       NA
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau     5.0159     2.5882   1.938 0.052908 .  
## alpha   0.9369     0.1062   8.821  < 2e-16 ***
## A       2.7200     0.8084   3.365 0.000796 ***
## k     114.4827    24.7841   4.619 4.36e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.106 on 988 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 2.507e-06
##   (14 observations deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.93022, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -4.4269, p-value = 9.56e-06
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 4 rows containing missing values (`geom_point()`).
## Warning: Removed 1218 rows containing missing values (`geom_line()`).

plotting 2

M242 - Cascade Mixed Forest

Model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   3147     6340.4                                
## 2   3146     5972.5  1 367.87  193.78 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 14546.02
## 2     2 14359.74
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau    -1.73500    0.21775  -7.968 2.24e-15 ***
## alpha   1.01162    0.06536  15.477  < 2e-16 ***
## A      11.13446    0.85343  13.047  < 2e-16 ***
## k     136.14898    9.82982  13.851  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.378 on 3146 degrees of freedom
## 
## Number of iterations to convergence: 4 
## Achieved convergence tolerance: 3.142e-06
##   (74 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

Model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "a", "_TI", sep = "")), data = G_M242,  : 
##   parameters without starting value in 'data': tau, phi, DeltaPDSI
## Error in nls(get(paste("fg_", Mod.Sel1, "b", "_TI", sep = "")), data = G_M242,  : 
##   parameters without starting value in 'data': tau, phi, DeltaPDSI
## Error in nls(get(paste("fg_", Mod.Sel1, "c", "_TI", sep = "")), data = G_M242,  : 
##   parameters without starting value in 'data': tau, phi, DeltaPDSI
##   model      AIC
## 1     2 14359.74
## 2    2a       NA
## 3    2b       NA
## 4    2c       NA
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau    -1.73500    0.21775  -7.968 2.24e-15 ***
## alpha   1.01162    0.06536  15.477  < 2e-16 ***
## A      11.13446    0.85343  13.047  < 2e-16 ***
## k     136.14898    9.82982  13.851  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.378 on 3146 degrees of freedom
## 
## Number of iterations to convergence: 4 
## Achieved convergence tolerance: 3.142e-06
##   (74 observations deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.90075, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -5.1248, p-value = 2.978e-07
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 46 rows containing missing values (`geom_point()`).
## Warning: Removed 126 rows containing missing values (`geom_line()`).

plotting 2

M261 - Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow

Model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   1682     2218.6                                
## 2   1681     2092.8  1 125.76  101.02 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 6757.119
## 2     2 6660.790
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau    -1.15923    0.38534  -3.008  0.00267 ** 
## alpha   0.92459    0.08357  11.063  < 2e-16 ***
## A      12.07063    1.35120   8.933  < 2e-16 ***
## k     258.31415   25.56496  10.104  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.116 on 1681 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 3.359e-07
##   (292 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

Model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "a", "_TI", sep = "")), data = G_M261,  : 
##   parameters without starting value in 'data': tau, phi, DeltaPDSI
## Error in nls(get(paste("fg_", Mod.Sel1, "b", "_TI", sep = "")), data = G_M261,  : 
##   parameters without starting value in 'data': tau, phi, DeltaPDSI
## Error in nls(get(paste("fg_", Mod.Sel1, "c", "_TI", sep = "")), data = G_M261,  : 
##   parameters without starting value in 'data': tau, phi, DeltaPDSI
##   model     AIC
## 1     2 6660.79
## 2    2a      NA
## 3    2b      NA
## 4    2c      NA
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau    -1.15923    0.38534  -3.008  0.00267 ** 
## alpha   0.92459    0.08357  11.063  < 2e-16 ***
## A      12.07063    1.35120   8.933  < 2e-16 ***
## k     258.31415   25.56496  10.104  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.116 on 1681 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 3.359e-07
##   (292 observations deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.90309, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -2.6679, p-value = 0.007632
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 154 rows containing missing values (`geom_point()`).

plotting 2

M262 - Califormia Coastal Range = Coniferous Forest - Open woodland Shrub Meadow

Model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

Model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M313 - Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow

Model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1    363     161.29                                
## 2    362     138.69  1 22.599  58.988 1.498e-13 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 797.8815
## 2     2 744.6298
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    -2.4082     0.2569  -9.373  < 2e-16 ***
## alpha   0.8997     0.1025   8.781  < 2e-16 ***
## A      12.8332     2.7013   4.751 2.93e-06 ***
## k     245.1081    64.9200   3.776 0.000187 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.619 on 362 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 2.09e-06
##   (1 observation deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

Model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "a", "_TI", sep = "")), data = G_M313,  : 
##   parameters without starting value in 'data': tau, phi, DeltaPDSI
## Error in nls(get(paste("fg_", Mod.Sel1, "b", "_TI", sep = "")), data = G_M313,  : 
##   parameters without starting value in 'data': tau, phi, DeltaPDSI
## Error in nls(get(paste("fg_", Mod.Sel1, "c", "_TI", sep = "")), data = G_M313,  : 
##   parameters without starting value in 'data': tau, phi, DeltaPDSI
##   model      AIC
## 1     2 744.6298
## 2    2a       NA
## 3    2b       NA
## 4    2c       NA
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    -2.4082     0.2569  -9.373  < 2e-16 ***
## alpha   0.8997     0.1025   8.781  < 2e-16 ***
## A      12.8332     2.7013   4.751 2.93e-06 ***
## k     245.1081    64.9200   3.776 0.000187 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.619 on 362 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 2.09e-06
##   (1 observation deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.97345, p-value = 3.017e-06
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -1.1458, p-value = 0.2519
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 1183 rows containing missing values (`geom_line()`).

plotting 2

M331 - Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow

Model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   1732     1220.2                                
## 2   1731     1096.0  1 124.22   196.2 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 4008.309
## 2     2 3824.022
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    0.68604    1.04125   0.659     0.51    
## alpha  0.85623    0.05023  17.047  < 2e-16 ***
## A      2.15238    0.44063   4.885 1.13e-06 ***
## k     93.67208   13.89544   6.741 2.13e-11 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7957 on 1731 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 3.555e-06
##   (21 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

Model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "a", "_TI", sep = "")), data = G_M331,  : 
##   parameters without starting value in 'data': tau, phi, DeltaPDSI
## Error in nls(get(paste("fg_", Mod.Sel1, "b", "_TI", sep = "")), data = G_M331,  : 
##   parameters without starting value in 'data': tau, phi, DeltaPDSI
## Error in nls(get(paste("fg_", Mod.Sel1, "c", "_TI", sep = "")), data = G_M331,  : 
##   parameters without starting value in 'data': tau, phi, DeltaPDSI
##   model      AIC
## 1     2 3824.022
## 2    2a       NA
## 3    2b       NA
## 4    2c       NA
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    0.68604    1.04125   0.659     0.51    
## alpha  0.85623    0.05023  17.047  < 2e-16 ***
## A      2.15238    0.44063   4.885 1.13e-06 ***
## k     93.67208   13.89544   6.741 2.13e-11 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7957 on 1731 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 3.555e-06
##   (21 observations deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.86593, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -4.9821, p-value = 6.29e-07
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 10 rows containing missing values (`geom_point()`).
## Warning: Removed 1091 rows containing missing values (`geom_line()`).

plotting 2

M332 - Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow

Model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   2513     1908.3                                
## 2   2512     1605.4  1 302.97  474.07 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 7070.262
## 2     2 6637.298
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau    -1.26573    0.28817  -4.392 1.17e-05 ***
## alpha   1.02015    0.03978  25.645  < 2e-16 ***
## A       7.81968    0.82996   9.422  < 2e-16 ***
## k     172.60172   17.04495  10.126  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7994 on 2512 degrees of freedom
## 
## Number of iterations to convergence: 9 
## Achieved convergence tolerance: 5.624e-06
##   (96 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

Model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "a", "_TI", sep = "")), data = G_M332,  : 
##   parameters without starting value in 'data': tau, phi, DeltaPDSI
## Error in nls(get(paste("fg_", Mod.Sel1, "b", "_TI", sep = "")), data = G_M332,  : 
##   parameters without starting value in 'data': tau, phi, DeltaPDSI
## Error in nls(get(paste("fg_", Mod.Sel1, "c", "_TI", sep = "")), data = G_M332,  : 
##   parameters without starting value in 'data': tau, phi, DeltaPDSI
##   model      AIC
## 1     2 6637.298
## 2    2a       NA
## 3    2b       NA
## 4    2c       NA
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau    -1.26573    0.28817  -4.392 1.17e-05 ***
## alpha   1.02015    0.03978  25.645  < 2e-16 ***
## A       7.81968    0.82996   9.422  < 2e-16 ***
## k     172.60172   17.04495  10.126  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7994 on 2512 degrees of freedom
## 
## Number of iterations to convergence: 9 
## Achieved convergence tolerance: 5.624e-06
##   (96 observations deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.89792, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -5.4149, p-value = 6.132e-08
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 53 rows containing missing values (`geom_point()`).
## Warning: Removed 1001 rows containing missing values (`geom_line()`).

plotting 2

M333 - Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow

Model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   1691     1694.2                                
## 2   1690     1407.8  1 286.39  343.79 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 5853.124
## 2     2 5541.443
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.73546    0.93704   0.785    0.433    
## alpha   1.04434    0.04862  21.479  < 2e-16 ***
## A       5.89925    1.08977   5.413 7.07e-08 ***
## k     138.46540   14.07628   9.837  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9127 on 1690 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 9.943e-06
##   (59 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

Model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "a", "_TI", sep = "")), data = G_M333,  : 
##   parameters without starting value in 'data': tau, phi, DeltaPDSI
## Error in nls(get(paste("fg_", Mod.Sel1, "b", "_TI", sep = "")), data = G_M333,  : 
##   parameters without starting value in 'data': tau, phi, DeltaPDSI
## Error in nls(get(paste("fg_", Mod.Sel1, "c", "_TI", sep = "")), data = G_M333,  : 
##   parameters without starting value in 'data': tau, phi, DeltaPDSI
##   model      AIC
## 1     2 5541.443
## 2    2a       NA
## 3    2b       NA
## 4    2c       NA
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.73546    0.93704   0.785    0.433    
## alpha   1.04434    0.04862  21.479  < 2e-16 ***
## A       5.89925    1.08977   5.413 7.07e-08 ***
## k     138.46540   14.07628   9.837  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9127 on 1690 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 9.943e-06
##   (59 observations deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.91917, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -4.2412, p-value = 2.223e-05
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 25 rows containing missing values (`geom_point()`).
## Warning: Removed 925 rows containing missing values (`geom_line()`).

plotting 2

M334 - Black Hills Coniferous Forest

Model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1    355     278.17                                
## 2    354     253.55  1  24.62  34.374 1.043e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 925.8321
## 2     2 894.6559
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    -0.1267     1.1013  -0.115 0.908493    
## alpha   0.8505     0.1276   6.665 1.02e-10 ***
## A       2.3576     0.5852   4.029 6.87e-05 ***
## k      44.1368    12.9692   3.403 0.000742 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8463 on 354 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 2.009e-06
##   (101 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

Model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "a", "_TI", sep = "")), data = G_M334,  : 
##   parameters without starting value in 'data': tau, phi, DeltaPDSI
## Error in nls(get(paste("fg_", Mod.Sel1, "b", "_TI", sep = "")), data = G_M334,  : 
##   parameters without starting value in 'data': tau, phi, DeltaPDSI
## Error in nls(get(paste("fg_", Mod.Sel1, "c", "_TI", sep = "")), data = G_M334,  : 
##   parameters without starting value in 'data': tau, phi, DeltaPDSI
##   model      AIC
## 1     2 894.6559
## 2    2a       NA
## 3    2b       NA
## 4    2c       NA
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     tau/100) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    -0.1267     1.1013  -0.115 0.908493    
## alpha   0.8505     0.1276   6.665 1.02e-10 ***
## A       2.3576     0.5852   4.029 6.87e-05 ***
## k      44.1368    12.9692   3.403 0.000742 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8463 on 354 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 2.009e-06
##   (101 observations deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.92289, p-value = 1.3e-12
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -1.998, p-value = 0.04572
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 46 rows containing missing values (`geom_point()`).
## Warning: Removed 1264 rows containing missing values (`geom_line()`).

plotting 2

M341 - Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow

Model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

Model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2


Fitted parameters

Best / selected models by ecoprovince

Code Ecoregion Sel.Mod
211 Northeastern Mixed Forest 2
212 Laurentian Mixed Forest 2
221 Eastern Broadleaf Forest 2
222 Midwest Broadleaf Forest 2
223 Central Interior Broadleaf Forest 2
231 Southeastern Mixed Forest 2
232 Outer Coastal Plain Mixed Forest 2
234 Lower Mississippi Riverine Forest 2
242 Pacific Lowland Mixed Forest 2
251 Prairie Parkland (Temperate) 2
255 Prairie Parkland (Subtropical) NA
261 California Coastal Chaparral Forest and Shrub NA
262 California Dry Steppe NA
263 California Coastal Steppe - Mixed Forest and Redwood Forest NA
313 Colorado Plateau Semi-Desert 2
315 Southwest Plateau and Plains Dry Steppe and Shrub NA
321 Chihuahuan Semi-Desert NA
322 American Semidesert and Desert NA
331 Great Plains/Palouse Dry Steppe NA
332 Great Plains Steppe 2
341 Intermountain Semi-Desert and Desert NA
342 Intermountain Semi-Desert 2
411 Everglades NA
M211 Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow 2
M221 Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow 2
M223 Ozark Broadleaf Forest Meadow 2
M231 Ouachita Mixed Forest 2
M242 Cascade Mixed Forest 2
M261 Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow 2
M262 California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow NA
M313 Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow 2
M331 Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow 2
M332 Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow 2
M333 Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow 2
M334 Black Hills Coniferous Forest 2
M341 Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow NA

table by ecoprovince

Code Ecoregion region n.obs n.plots tau tau.variance tau.2.5 tau.97.5 alpha alpha.variance alpha.2.5 alpha.97.5 A A.2.5 A.97.5 k k.2.5 k.97.5
211 Northeastern Mixed Forest east 6877 2876 0.5560549 NA 0.1957426 0.9163672 0.7961287 NA 0.7338538 0.8584037 4.925631 4.5213459 5.329917 113.43273 102.90326 123.96221
212 Laurentian Mixed Forest east 22715 9499 1.1569991 0.0229510 0.8600536 1.4539446 1.0693906 0.0003781 1.0312759 1.1075053 5.573636 5.1836245 5.963647 213.12553 197.20902 229.04204
221 Eastern Broadleaf Forest east 7333 3571 -0.9302528 0.0122539 -1.1472514 -0.7132542 0.8226072 0.0013171 0.7514632 0.8937511 7.022411 6.4906234 7.554200 89.63813 78.48379 100.79246
222 Midwest Broadleaf Forest east 5845 2589 0.2268005 0.0423833 -0.1768023 0.6304033 0.9716370 0.0014746 0.8963549 1.0469190 6.841671 6.1293169 7.554025 141.35101 124.32769 158.37433
223 Central Interior Broadleaf Forest east 10010 3864 -0.9866708 0.0088774 -1.1713637 -0.8019779 0.8487235 0.0012289 0.7800073 0.9174397 11.868828 10.5383536 13.199302 263.34595 224.72766 301.96423
231 Southeastern Mixed Forest east 13517 6193 1.5531887 0.0385956 1.1681035 1.9382739 0.9388297 0.0004387 0.8977761 0.9798833 5.087821 4.7357566 5.439886 62.69065 57.19405 68.18724
232 Outer Coastal Plain Mixed Forest east 13629 6626 1.1066026 0.0361284 0.7340291 1.4791760 0.9624493 0.0004221 0.9221786 1.0027200 5.289786 4.9074756 5.672097 68.64871 62.76319 74.53423
234 Lower Mississippi Riverine Forest east 1388 778 2.2159042 1.7228309 -0.3590346 4.7908430 0.9884607 0.0083077 0.8096528 1.1672686 4.125290 2.5076923 5.742887 56.92517 36.49536 77.35498
242 Pacific Lowland Mixed Forest pacific 83 83 1.6579938 13.9067684 -5.7693078 9.0852954 0.7566029 0.0739823 0.2148743 1.2983314 6.246946 -1.0823477 13.576240 90.62213 35.41388 145.83037
251 Prairie Parkland (Temperate) east 2295 906 0.6811323 0.1817401 -0.1549870 1.5172516 0.5486749 0.0081933 0.3711442 0.7262055 4.546017 3.6783426 5.413690 98.08080 74.73861 121.42298
255 Prairie Parkland (Subtropical) east 717 319 NA NA NA NA NA NA NA NA NA NA NA NA NA NA
261 California Coastal Chaparral Forest and Shrub pacific 25 25 NA NA NA NA NA NA NA NA NA NA NA NA NA NA
262 California Dry Steppe pacific 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA
263 California Coastal Steppe - Mixed Forest and Redwood Forest pacific 163 161 NA NA NA NA NA NA NA NA NA NA NA NA NA NA
313 Colorado Plateau Semi-Desert interior west 218 218 -0.7113609 1.5391215 -3.1569456 1.7342238 0.9557811 0.0576489 0.4824754 1.4290868 4.548433 1.0582364 8.038630 189.58218 56.48993 322.67444
315 Southwest Plateau and Plains Dry Steppe and Shrub interior west 4 4 NA NA NA NA NA NA NA NA NA NA NA NA NA NA
321 Chihuahuan Semi-Desert interior west 9 9 NA NA NA NA NA NA NA NA NA NA NA NA NA NA
322 American Semidesert and Desert interior west 3 3 NA NA NA NA NA NA NA NA NA NA NA NA NA NA
331 Great Plains/Palouse Dry Steppe interior west 331 255 NA NA NA NA NA NA NA NA NA NA NA NA NA NA
332 Great Plains Steppe interior west 232 128 1.7278114 5.2292244 -2.7825658 6.2381886 0.7985898 0.0619002 0.3078623 1.2893172 4.203556 0.8602713 7.546841 144.41344 47.71849 241.10839
341 Intermountain Semi-Desert and Desert interior west 66 64 NA NA NA NA NA NA NA NA NA NA NA NA NA NA
342 Intermountain Semi-Desert interior west 124 123 1.0856593 12.2095842 -5.8383739 8.0096926 1.0512953 0.0419176 0.6455933 1.4569974 5.180998 -1.5161196 11.878116 176.68258 35.43605 317.92912
411 Everglades east 96 63 NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M211 Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow east 6772 3006 1.3789562 0.0716694 0.8541573 1.9037551 0.8139561 0.0008829 0.7557064 0.8722058 3.719861 3.3429453 4.096776 104.43455 93.90666 114.96245
M221 Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow east 8315 3810 0.3103333 0.0315639 -0.0379292 0.6585959 0.8859613 0.0028000 0.7822337 0.9896889 5.649565 5.1102120 6.188918 105.48995 89.97177 121.00812
M223 Ozark Broadleaf Forest Meadow east 896 349 3.5517264 3.3238593 -0.0264611 7.1299139 1.0186753 0.0240896 0.7140564 1.3232942 2.756220 1.2985300 4.213910 114.70220 50.69580 178.70860
M231 Ouachita Mixed Forest east 1006 495 5.0158823 6.6986410 -0.0630660 10.0948307 0.9368876 0.0112811 0.7284593 1.1453160 2.720020 1.1336037 4.306437 114.48270 65.84720 163.11820
M242 Cascade Mixed Forest pacific 3224 3207 -1.7349981 0.0474142 -2.1619407 -1.3080556 1.0116170 0.0042722 0.8834609 1.1397730 11.134460 9.4611196 12.807800 136.14898 116.87547 155.42249
M261 Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow pacific 1977 1807 -1.1592275 0.1484890 -1.9150294 -0.4034256 0.9245881 0.0069847 0.7606675 1.0885086 12.070635 9.4204317 14.720838 258.31415 208.17166 308.45665
M262 California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow interior west 30 26 NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M313 Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow interior west 367 367 -2.4081804 0.0660097 -2.9134306 -1.9029302 0.8996779 0.0104966 0.6982007 1.1011551 12.833247 7.5211319 18.145361 245.10807 117.44044 372.77570
M331 Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow interior west 1756 1756 0.6860443 1.0841993 -1.3561940 2.7282827 0.8562318 0.0025230 0.7577159 0.9547477 2.152384 1.2881539 3.016615 93.67208 66.41846 120.92569
M332 Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow interior west 2612 2602 -1.2657294 0.0830425 -1.8308064 -0.7006525 1.0201463 0.0015824 0.9421415 1.0981511 7.819684 6.1921981 9.447169 172.60172 139.17812 206.02531
M333 Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow interior west 1753 1742 0.7354562 0.8780488 -1.1024298 2.5733421 1.0443357 0.0023640 0.9489728 1.1396987 5.899254 3.7618186 8.036690 138.46540 110.85662 166.07419
M334 Black Hills Coniferous Forest interior west 459 181 -0.1266700 1.2128070 -2.2925346 2.0391945 0.8505473 0.0162865 0.5995614 1.1015331 2.357583 1.2066361 3.508530 44.13678 18.63034 69.64322
M341 Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow interior west 220 220 NA NA NA NA NA NA NA NA NA NA NA NA NA NA

plot tau

map

## OGR data source with driver: ESRI Shapefile 
## Source: "C:\Users\hogan.jaaron\Dropbox\FIA_R\Mapping\S_USA.EcoMapProvinces\S_USA.EcoMapProvinces.shp", layer: "S_USA.EcoMapProvinces"
## with 37 features
## It has 17 fields
## Integer64 fields read as strings:  PROVINCE_ PROVINCE_I
## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

plot alpha (biomass growth compensation effect)

plot A (asymptote of forest biomass growth in Mg/ha/yr)

## Warning: Removed 12 rows containing missing values (`geom_point()`).

plot k (stand biomass at half biomss G in Mg/ha)

## Warning: Removed 12 rows containing missing values (`geom_point()`).

Caclulations - weighted averages

tau (productivity trend (in %) 2000-2021)

##          region weighted.tau weighted.tau.std_Error 95 % CI, upper
## 1     entire US   0.43761120             0.12962494     0.69167607
## 2       pacific  -0.12984462             0.01866564    -0.09325997
## 3          east   0.59360480             0.11934977     0.82753035
## 4 interior west  -0.02614898             0.04700905     0.06598875
##   95 % CI, lower
## 1      0.1835463
## 2     -0.1664293
## 3      0.3596793
## 4     -0.1182867

alpha (effect of DeltaPDSI)

##          region weighted.phi weighted.phi.std_Error 95 % CI, upper
## 1     entire US            0                      0              0
## 2       pacific            0                      0              0
## 3          east            0                      0              0
## 4 interior west            0                      0              0
##   95 % CI, lower
## 1              0
## 2              0
## 3              0
## 4              0

A (asymptote of forest biomass growth in Mg/ha/yr)

##          region weighted.A
## 1     entire US   6.291036
## 2       pacific  10.985869
## 3          east   5.888741
## 4 interior west   5.417810

K (stand biomass at half biomss G in Mg/ha)

##          region weighted.k
## 1     entire US   134.4559
## 2       pacific   172.4257
## 3          east   130.0094
## 4 interior west   134.3588